Who said: “The Superfund legislation... may prove to be as far-reaching and important as any accomplishment of my administration. The reduction of the threat to America's health and safety from thousands of toxic-waste sites will continue to be an urgent…issue …”

'Unless,' said I [Socrates], either philosophers become kings in our states or those whom we now call our kings:. and rulers take to the pursuit of' philosophy seriously and adequately, and there is a conjunction of these two things, political power and philosophic intelligence, while the motley horde of the natures who at present pursue either apart from the other are compulsorily excluded, there can be no cessation of troubles, dear Glaucon, for our states, nor, I fancy for the human race either. Nor, until this happens, will this constitution which we have been expounding in theory ever be put into practice within the limits of possibility and see the light of the sun.

... one of the main functions of an analogy or model is to suggest extensions of the theory by considering extensions of the analogy, since more is known about the analogy than is known about the subject matter of the theory itself … A collection of observable concepts in a purely formal hypothesis suggesting no analogy with anything would consequently not suggest either any directions for its own development.

... there is an external world which can in principle be exhaustively described in scientific language. The scientist, as both observer and language-user, can capture the external facts of the world in prepositions that are true if they correspond to the facts and false if they do not. Science is ideally a linguistic system in which true propositions are in one-to-one relation to facts, including facts that are not directly observed because they involve hidden entities or properties, or past events or far distant events. These hidden events are described in theories, and theories can be inferred from observation, that is the hidden explanatory mechnism of the world can be discovered from what is open to observation. Man as scientist is regarded as standing apart from the world and able to experiment and theorize about it objectively and dispassionately.

Dilbert: It took weeks but I’ve calculated a new theory about the origin of the universe. According to my calculations it didn’t start with a “Big Bang” at all—it was more of “Phhbwt” sound. You may be wondering about the practical applications of the “Little Phhbwt” theory.Dogbert: I was wondering when you’ll go away.

Dilbert: You joined the “Flat Earth Society?”Dogbert: I believe the earth must be flat. There is no good evidence to support the so-called “round earth theory.”Dilbert: I think Christopher Columbus would disagree.Dogbert: How convenient that your best witness is dead.

Discovery always carries an honorific connotation. It is the stamp of approval on a finding of lasting value. Many laws and theories have come and gone in the history of science, but they are not spoken of as discoveries. Kepler is said to have discovered the laws of planetary motion named after him, but no the many other 'laws' which he formulated. ... Theories are especially precarious, as this century profoundly testifies. World views can and do often change. Despite these difficulties, it is still true that to count as a discovery a finding must be of at least relatively permanent value, as shown by its inclusion in the generally accepted body of scientific knowledge.

Dogbert: So, Since Columbus is dead, you have no evidence that the earth is round.Dilbert: Look. You can Ask Senator John Glenn. He orbited the earth when he was an astronaut.Dogbert: So, your theory depends on the honesty of politicians.Dilbert: Yes... no, wait...

La chaleur pénètre, comme la gravité, toutes les substances de l’univers, ses rayons occupent toutes les parties de l’espace. Le but de notre ouvrage est d’exposer les lois mathématiques que suit cet élément. Cette théorie formera désormais une des branches les plus importantes de la physique générale.Heat, like gravity, penetrates every substance of the universe, its rays occupy all parts of space. The object of our work is to set forth the mathematical laws which this element obeys. The theory of heat will hereafter form one of the most important branches of general physics.

La théorie des séries infinies en général est justqu’à présent très mal fondée. On applique aux séries infinies toutes les opérations, come si elles aient finies; mais cela est-il bien permis? Je crois que non. Où est-il démonstré qu/on ontient la différentielle dune série infinie en prenant la différentiaella de chaque terme. Rien n’est plus facile que de donner des exemples où cela n’est pas juste.Until now the theory of infinite series in general has been very badly grounded. One applies all the operations to infinite series as if they were finite; but is that permissible? I think not. Where is it demonstrated that one obtains the differential of an infinite series by taking the differential of each term? Nothing is easier than to give instances where this is not so.

La théorie est l’hypothèse vérifiée, après qu’elle a été soumise au contrôle du raisonnement et de la critique expérimentale. La meilleure théorie est celle qui a été vérifiée par le plus grand nombre de faits. Mais une théorie, pour rester bonne, doit toujours se modifier avec les progrès de la science et demeurer constamment soumise à la vérification et à la critique des faits nouveaux qui apparaissent.A theory is a verified hypothesis, after it has been submitted to the control of reason and experimental criticism. The soundest theory is one that has been verified by the greatest number of facts. But to remain valid, a theory must be continually altered to keep pace with the progress of science and must be constantly resubmitted to verification and criticism as new facts appear.

Original work in French, Introduction à l'Étude de la Médecine Expérimentale (1865), 385. English translation by Henry Copley Green in An Introduction to the Study of Experimental Medicine (1927, 1957), 220.

Original work in French, Introduction à l'Étude de la Médecine Expérimentale (1865), 40. English translation by Henry Copley Green in An Introduction to the Study of Experimental Medicine (1927, 1957), 26.

Ron Hutcheson, a Knight-Ridder reporter: [Mr. President, what are your] personal views [about the theory of] intelligent design?President George W. Bush: [Laughing. You're] doing a fine job of dragging me back to the past [days as governor of Texas]. ... Then, I said that, first of all, that decision should be made to local school districts, but I felt like both sides ought to be properly taught...”Hutcheson: Both sides ought to be properly taught?President: Yes ... so people can understand what the debate is about.Hutcheson: So the answer accepts the validity of “intelligent design” as an alternative to evolution?President: I think that part of education is to expose people to different schools of thought, and I'm not suggesting—you're asking me whether or not people ought to be exposed to different ideas, and the answer is yes.Hutcheson: So we've got to give these groups—...President: [interrupting] Very interesting question, Hutch. [Laughter from other reporters]

From conversation with reporters at the White House (1 Aug 2005), as quoted by Matthew Cooper in 'Fanning the Controversy Over “Intelligent Design”', Time (3 Aug 2005). The Time writer stated, “The president has gone farther in questioning the widely-taught theories of evolution and natural selection than any president since Ronald Reagan, who advocated teaching creationism in public schools alongside evolution.” Just a few months later, in the nation's first case on that point, on 20 Dec 2005, “a federal judge [John E. Jones] ruled it was unconstitutional for a Pennsylvania school district to present intelligent design as an alternative in high school biology courses, because it is a religious viewpoint,” as reported by Laurie Goodstein in 'Judge Rejects Teaching Intelligent Design', New York Times (21 Dec 2005). Goodstein also wrote “Judge Jones, a Republican appointed by President Bush, concluded that intelligent design was not science,” and that “the evidence in the trial proved that intelligent design was 'creationism relabeled.' The Supreme Court has already ruled that creationism ... cannot be taught as science in a public school.”

Von Theorie wild man nicht heller.Gott geb' täglich unsern Teller.When theory's light is less than stellar.Give us, O Lord, our daily Teller.This rhyme from an alphabet ditty describing various physicists was written for a party at Göttingen.

Quoted in Edward Teller with Judith L. Shoolery, Memoirs: A Twentieth-Century Journey in Science and Politics (2001), 75. The first phrase, translated more literally than poetically, is given as, 'When theory does not enlighten us,' in Nina Byers and Gary Williams, Out of the Shadows (2006),130.

[In refutation of evolution] There is not enough evidence, consistent evidence to make it as fact, and I say that because for theory to become a fact, it needs to consistently have the same results after it goes through a series of tests. The tests that they put—that they use to support evolution do not have consistent results. Now too many people are blindly accepting evolution as fact. But when you get down to the hard evidence, it’s merely a theory.[In favor of the teaching of creationism alongside evolution in schools.]

A closer look at the course followed by developing theory reveals for a start that it is by no means as continuous as one might expect, but full of breaks and at least apparently not along the shortest logical path. Certain methods often afforded the most handsome results only the other day, and many might well have thought that the development of science to infinity would consist in no more than their constant application. Instead, on the contrary, they suddenly reveal themselves as exhausted and the attempt is made to find other quite disparate methods. In that event there may develop a struggle between the followers of the old methods and those of the newer ones. The former's point of view will be termed by their opponents as out-dated and outworn, while its holders in turn belittle the innovators as corrupters of true classical science.

A conceptual scheme is never discarded merely because of a few stubborn facts with which it cannot be reconciled; a conceptual scheme is either modified or replaced by a better one, never abandoned with nothing left to take its place.

A discovery in science, or a new theory, even when it appears most unitary and most all-embracing, deals with some immediate element of novelty or paradox within the framework of far vaster, unanalysed, unarticulated reserves of knowledge, experience, faith, and presupposition. Our progress is narrow; it takes a vast world unchallenged and for granted. This is one reason why, however great the novelty or scope of new discovery, we neither can, nor need, rebuild the house of the mind very rapidly. This is one reason why science, for all its revolutions, is conservative. This is why we will have to accept the fact that no one of us really will ever know very much. This is why we shall have to find comfort in the fact that, taken together, we know more and more.

A man who is all theory is like “a rudderless ship on a shoreless sea.” ... Theories and speculations may be indulged in with safety only as long as they are based on facts that we can go back to at all times and know that we are on solid ground.

A scientifically unimportant discovery is one which, however true and however interesting for other reasons, has no consequences for a system of theory with which scientists in that field are concerned.

A taxonomy of abilities, like a taxonomy anywhere else in science, is apt to strike a certain type of impatient student as a gratuitous orgy of pedantry. Doubtless, compulsions to intellectual tidiness express themselves prematurely at times, and excessively at others, but a good descriptive taxonomy, as Darwin found in developing his theory, and as Newton found in the work of Kepler, is the mother of laws and theories.

A theory is a supposition which we hope to be true, a hypothesis is a supposition which we expect to be useful; fictions belong to the realm of art; if made to intrude elsewhere, they become either make-believes or mistakes.

As quoted by William Ramsay, in 'Radium and Its Products', Harper’s Magazine (Dec 1904), 52. The first part, about suppositions, appears in a paper read by G. Johnson Stoney to the American Philosophical Society, Philadelphia (3 Apr 1903), printed in 'On the Dependence of What Apparently Takes Place in Nature Upon What Actually Occurs in the Universe of Real Existences', Proceedings of the American Philosophical Society Held at Philadelphia for Promoting Useful Knowledge (Apr-May 1903) 42, No. 173, 107. If you know a primary source for the part on fictions and mistakes, please contact Webmaster.

A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me. It is the only physical theory of universal content concerning which I am convinced that within the framework of the applicability of its basic concepts, it will never be overthrown.

A … difference between most system-building in the social sciences and systems of thought and classification of the natural sciences is to be seen in their evolution. In the natural sciences both theories and descriptive systems grow by adaptation to the increasing knowledge and experience of the scientists. In the social sciences, systems often issue fully formed from the mind of one man. Then they may be much discussed if they attract attention, but progressive adaptive modification as a result of the concerted efforts of great numbers of men is rare.

About thirty years ago there was much talk that geologists ought only to observe and not theorise; and I well remember some one saying that at this rate a man might as well go into a gravel-pit and count the pebbles and describe the colours. How odd it is that anyone should not see that all observation must be for or against some view if it is to be of any service!

According to the theory of aerodynamics, as may be readily demonstrated through wind tunnel experiments, the bumblebee is unable to fly. This is because the size, weight and shape of his body in relation to the total wingspread make flying impossible. But the bumblebee, being ignorant of these scientific truths, goes ahead and flies anyway—and makes a little honey every day.

Sign in a General Motors Corporation factory. As quoted in Ralph L. Woods, The Businessman's
Book of Quotations (1951), 249-50. Cited in Suzy Platt (ed)., Respectfully Quoted: A Dictionary of Quotations (1989), 118.

After the discovery of spectral analysis no one trained in physics could doubt the problem of the atom would be solved when physicists had learned to understand the language of spectra. So manifold was the enormous amount of material that has been accumulated in sixty years of spectroscopic research that it seemed at first beyond the possibility of disentanglement. An almost greater enlightenment has resulted from the seven years of Röntgen spectroscopy, inasmuch as it has attacked the problem of the atom at its very root, and illuminates the interior. What we are nowadays hearing of the language of spectra is a true 'music of the spheres' in order and harmony that becomes ever more perfect in spite of the manifold variety. The theory of spectral lines will bear the name of Bohr for all time. But yet another name will be permanently associated with it, that of Planck. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei.

All good intellects have repeated, since Bacon’s time, that there can be no real knowledge but that which is based on observed facts. This is incontestable, in our present advanced stage; but, if we look back to the primitive stage of human knowledge, we shall see that it must have been otherwise then. If it is true that every theory must be based upon observed facts, it is equally true that facts cannot be observed without the guidance of some theory. Without such guidance, our facts would be desultory and fruitless; we could not retain them: for the most part we could not even perceive them.

All scientific theories are provisional and may be changed, but ... on the whole, they are accepted from Washington to Moscow because of their practical success. Where religion has opposed the findings of science, it has almost always had to retreat.

All that stuff I was taught about evolution, embryology, Big Bang theory, all that is lies straight from the pit of hell. It’s lies to try to keep me and all the folks who are taught that from understanding that they need a savior.[Revealing his anti-science views, contrary to the qualifications needed to make important public policy on matters of science.]

Almost everyone... seems to be quite sure that the differences between the methodologies of history and of the natural sciences are vast. For, we are assured, it is well known that in the natural sciences we start from observation and proceed by induction to theory. And is it not obvious that in history we proceed very differently? Yes, I agree that we proceed very differently. But we do so in the natural sciences as well.In both we start from myths—from traditional prejudices, beset with error—and from these we proceed by criticism: by the critical elimination of errors. In both the role of evidence is, in the main, to correct our mistakes, our prejudices, our tentative theories—that is, to play a part in the critical discussion, in the elimination of error. By correcting our mistakes, we raise new problems. And in order to solve these problems, we invent conjectures, that is, tentative theories, which we submit to critical discussion, directed towards the elimination of error.

Anyone who has examined into the history of the theories of earth evolution must have been astounded to observe the manner in which the unique and the difficultly explainable has been made to take the place of the common and the natural in deriving the framework of these theories.

As every circumstance relating to so capital a discovery as this (the greatest, perhaps, that has been made in the whole compass of philosophy, since the time of Sir Isaac Newton) cannot but give pleasure to all my readers, I shall endeavour to gratify them with the communication of a few particulars which I have from the best authority. The Doctor [Benjamin Franklin], after having published his method of verifying his hypothesis concerning the sameness of electricity with the matter lightning, was waiting for the erection of a spire in Philadelphia to carry his views into execution; not imagining that a pointed rod, of a moderate height, could answer the purpose; when it occurred to him, that, by means of a common kite, he could have a readier and better access to the regions of thunder than by any spire whatever. Preparing, therefore, a large silk handkerchief, and two cross sticks, of a proper length, on which to extend it, he took the opportunity of the first approaching thunder storm to take a walk into a field, in which there was a shed convenient for his purpose. But dreading the ridicule which too commonly attends unsuccessful attempts in science, he communicated his intended experiment to no body but his son, who assisted him in raising the kite.The kite being raised, a considerable time elapsed before there was any appearance of its being electrified. One very promising cloud passed over it without any effect; when, at length, just as he was beginning to despair of his contrivance, he observed some loose threads of the hempen string to stand erect, and to avoid one another, just as if they had been suspended on a common conductor. Struck with this promising appearance, he inmmediately presented his knuckle to the key, and (let the reader judge of the exquisite pleasure he must have felt at that moment) the discovery was complete. He perceived a very evident electric spark. Others succeeded, even before the string was wet, so as to put the matter past all dispute, and when the rain had wetted the string, he collected electric fire very copiously. This happened in June 1752, a month after the electricians in France had verified the same theory, but before he had heard of any thing that they had done.

As far as I see, such a theory [of the primeval atom] remains entirely outside any metaphysical or religious question. It leaves the materialist free to deny any transcendental Being. He may keep, for the bottom of space-time, the same attitude of mind he has been able to adopt for events occurring in non-singular places in space-time. For the believer, it removes any attempt to familiarity with God, as were Laplace's chiquenaude or Jeans' finger. It is consonant with the wording of Isaiah speaking of the 'Hidden God' hidden even in the beginning of the universe ... Science has not to surrender in face of the Universe and when Pascal tries to infer the existence of God from the supposed infinitude of Nature, we may think that he is looking in the wrong direction.

'The Primeval atom Hypothesis and the Problem of Clusters of Galaxies', in R. Stoops (ed.), La Structure et l'Evolution de l'Univers (1958), 1-32. Trans. Helge Kragh, Cosmology and Controversy: The Historical Development of Two Theories of the Universe (1996), 60.

As is well known the principle of virtual velocities transforms all statics into a mathematical assignment, and by D'Alembert's principle for dynamics, the latter is again reduced to statics. Although it is is very much in order that in gradual training of science and in the instruction of the individual the easier precedes the more difficult, the simple precedes the more complicated, the special precedes the general, yet the min, once it has arrived at the higher standpoint, demands the reverse process whereby all statics appears only as a very special case of mechanics.

As soon … as it was observed that the stars retained their relative places, that the times of their rising and setting varied with the seasons, that sun, moon, and planets moved among them in a plane, … then a new order of things began.… Science had begun, and the first triumph of it was the power of foretelling the future; eclipses were perceived to recur in cycles of nineteen years, and philosophers were able to say when an eclipse was to be looked for. The periods of the planets were determined. Theories were invented to account for their eccentricities; and, false as those theories might be, the position of the planets could be calculated with moderate certainty by them.

Lecture delivered to the Royal Institution (5 Feb 1864), 'On the Science of History'. Collected in Notices of the Proceedings at the Meetings of the Members of the Royal Institution of Great Britain with Abstracts of the Discourses (1866), Vol. 4, 187.

Besides electrical engineering theory of the transmission of messages, there is a larger field [cybernetics] which includes not only the study of language but the study of messages as a means of controlling machinery and society, the development of computing machines and other such automata, certain reflections upon psychology and the nervous system, and a tentative new theory of scientific method.

Biological determinism is, in its essence, a theory of limits. It takes the current status of groups as a measure of where they should and must be ... We inhabit a world of human differences and predilections, but the extrapolation of these facts to theories of rigid limits is ideology.

Buffon, who, with all his theoretical ingenuity and extraordinary eloquence, I suspect had little actual information in the science on which he wrote so admirably For instance, he tells us that the cow sheds her horns every two years; a most palpable error. ... It is wonderful that Buffon who lived so much in the country at his noble seat should have fallen into such a blunder I suppose he has confounded the cow with the deer.

But although in theory physicists realize that their conclusions are ... not certainly true, this ... does not really sink into their consciousness. Nearly all the time ... they ... act as if Science were indisputably True, and what's more, as if only science were true.... Any information obtained otherwise than by the scientific method, although it may be true, the scientists will call “unscientific,” using this word as a smear word, by bringing in the connotation from its original [Greek] meaning, to imply that the information is false, or at any rate slightly phony.

But, contrary to the lady’s prejudices about the engineering profession, the fact is that quite some time ago the tables were turned between theory and applications in the physical sciences. Since World War II the discoveries that have changed the world are not made so much in lofty halls of theoretical physics as in the less-noticed labs of engineering and experimental physics. The roles of pure and applied science have been reversed; they are no longer what they were in the golden age of physics, in the age of Einstein, Schrödinger, Fermi and Dirac.

By an application of the theory of relativity to the taste of readers, today in Germany I am called a German man of science, and in England I am represented as a Swiss Jew. If I come to be regarded as a bête noire the descriptions will be reversed, and I shall become a Swiss Jew for the Germans and a German man of science for the English!

Chemistry and physics are experimental sciences; and those who are engaged in attempting to enlarge the boundaries of science by experiment are generally unwilling to publish speculations; for they have learned, by long experience, that it is unsafe to anticipate events. It is true, they must make certain theories and hypotheses. They must form some kind of mental picture of the relations between the phenomena which they are trying to investigate, else their experiments would be made at random, and without connection.

Chemistry is like a majestic skyscraper. The concrete secure foundation of chemistry consists of countless experimentally observed facts. The theories, principles and laws developed from these observations are like an elevator which runs from the bottom to the top of the edifice.

Considered in its entirety, psychoanalysis won’t do. It is an end product, moreover, like a dinosaur or a zeppelin, no better theory can ever be erected on its ruins, which will remain for ever one of the saddest and strangest of all landmarks in the history of twentieth century thought.

Cosmology, for centuries consisting of speculation based on a minimum of observational evidence and a maximum of philosophical predilection, became in the twentieth century an observational science, its theories now subject to verification or refutation to a degree previously unimaginable.

Darwin's theory was received in Russia with profound sympathy. While in Western Europe it met firmly established old traditions which it had first to overcome, in Russia its appearance coincided with the awakening of our society after the Crimean War and here it immediately received the status of full citizenship and ever since has enjoyed widespread popularity.

During my stay in London I resided for a considerable time in Clapham Road in the neighbourhood of Clapham Common... One fine summer evening I was returning by the last bus 'outside' as usual, through the deserted streets of the city, which are at other times so full of life. I fell into a reverie (Träumerei), and 10, the atoms were gambolling before my eyes! Whenever, hitherto, these diminutive beings had appeared to me, they had always been in motion: but up to that time I had never been able to discern the nature of their motion. Now, however, I saw how, frequently, two smaller atoms united to form a pair: how the larger one embraced the two smaller ones: how still larger ones kept hold of three or even four of the smaller: whilst the whole kept whirling in a giddy dance. I saw how the larger ones formed a chain, dragging the smaller ones after them but only at the ends of the chain. I saw what our past master, Kopp, my highly honoured teacher and friend has depicted with such charm in his Molekular-Welt: but I saw it long before him. The cry of the conductor 'Clapham Road', awakened me from my dreaming: but I spent part of the night in putting on paper at least sketches of these dream forms. This was the origin of the 'Structural Theory'.

From microfilmed Speaker's Copy of a radio script held at the BBC Written Archive Centre, for Hoyle's radio talk on the BBC Third Programme (28 Mar 1949). The date and time of the broadcast, 6:30pm, are given in that week’s Radio Times. The quote, with these references given in footnotes, in Simon Mitton, Fred Hoyle: A Life in Science (2011), 127-128 and 332. The text of the talk, the first printed use of the “big bang” expression, in the BBC’s The Listener magazine (7 Apr 1949), Vol.41, 568.

Electric and magnetic forces. May they live for ever, and never be forgot, if only to remind us that the science of electromagnetics, in spite of the abstract nature of its theory, involving quantities whose nature is entirely unknown at the present, is really and truly founded on the observations of real Newtonian forces, electric and magnetic respectively.

Engineering is the art of directing the great sources of power in nature for the use and the convenience of people. In its modern form engineering involves people, money, materials, machines, and energy. It is differentiated from science because it is primarily concerned with how to direct to useful and economical ends the natural phenomena which scientists discover and formulate into acceptable theories. Engineering therefore requires above all the creative imagination to innovate useful applications of natural phenomena. It seeks newer, cheaper, better means of using natural sources of energy and materials.

Engineers apply the theories and principles of science and mathematics to research and develop economical solutions to practical technical problems. Their work is the link between scientific discoveries and commercial applications. Engineers design products, the machinery to build those products, the factories in which those products are made, and the systems that ensure the quality of the product and efficiency of the workforce and manufacturing process. They design, plan, and supervise the construction of buildings, highways, and transit systems. They develop and implement improved ways to extract, process, and use raw materials, such as petroleum and natural gas. They develop new materials that both improve the performance of products, and make implementing advances in technology possible. They harness the power of the sun, the earth, atoms, and electricity for use in supplying the Nation’s power needs, and create millions of products using power. Their knowledge is applied to improving many things, including the
quality of health care, the safety of food products, and the efficient operation of financial systems.

Bureau of Labor Statistics, Occupational Outlook Handbook (2000) as quoted in Charles R. Lord. Guide to Information Sources in Engineering (2000), 5. This definition has been revised and expanded over time in different issues of the Handbook.

Entropy theory is indeed a first attempt to deal with global form; but it has not been dealing with structure. All it says is that a large sum of elements may have properties not found in a smaller sample of them.

Even mistaken hypotheses and theories are of use in leading to discoveries. This remark is true in all the sciences. The alchemists founded chemistry by pursuing chimerical problems and theories which are false. In physical science, which is more advanced than biology, we might still cite men of science who make great discoveries by relying on false theories. It seems, indeed, a necessary weakness of our mind to be able to reach truth only across a multitude of errors and obstacles.

Every discovery opens a new field for investigation of facts, shows us the imperfection of our theories. It has justly been said, that the greater the circle of light, the greater the boundary of darkness by which it is surrounded.

Every new theory as it arises believes in the flush of youth that it has the long sought goal; it sees no limits to its applicability, and believes that at last it is the fortunate theory to achieve the 'right' answer. This was true of electron theory—perhaps some readers will remember a book called The Electrical Theory of the Universe by de Tunzelman. It is true of general relativity theory with its belief that we can formulate a mathematical scheme that will extrapolate to all past and future time and the unfathomed depths of space. It has been true of wave mechanics, with its first enthusiastic claim a brief ten years ago that no problem had successfully resisted its attack provided the attack was properly made, and now the disillusionment of age when confronted by the problems of the proton and the neutron. When will we learn that logic, mathematics, physical theory, are all only inventions for formulating in compact and manageable form what we already know, like all inventions do not achieve complete success in accomplishing what they were designed to do, much less complete success in fields beyond the scope of the original design, and that our only justification for hoping to penetrate at all into the unknown with these inventions is our past experience that sometimes we have been fortunate enough to be able to push on a short distance by acquired momentum.

Evolution ... is really two theories, the vague theory and the precise theory. The vague theory has been abundantly proved.... The precise theory has never been proved at all. However, like relativity, it is accepted on faith.... On getting down to actual details, difficulties begin.

Facts alone, no matter how numerous or verifiable, do not automatically arrange themselves into an intelligible, or truthful, picture of the world. It is the task of the human mind to invent a theoretical framework to account for them.

Facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts. Facts do not go away while scientists debate rival theories for explaining them. Einstein's theory of gravitation replaced Newton's, but apples did not suspend themselves in mid-air pending the outcome.

Facts are of not much use, considered as facts. They bewilder by their number and their apparent incoherency. Let them be digested into theory, however, and brought into mutual harmony, and it is another matter.

Factual assertions and fundamental principles are... merely parts of theories: they are given within the framework of a theory; they are chosen and valid within this framework; and subsequently they are dependent upon it. This holds for all empirical sciences—for the natural sciences as well as those pertaining to history.

First... a new theory is attacked as absurd; then it is admitted to be true, but obvious and insignificant; finally it is seen to be so important that its adversaries claim that they themselves discovered it.

For if as scientists we seek simplicity, then obviously we try the simplest surviving theory first, and retreat from it only when it proves false. Not this course, but any other, requires explanation. If you want to go somewhere quickly, and several alternate routes are equally likely to be open, no one asks why you take the shortest. The simplest theory is to be chosen not because it is the most likely to be true but because it is scientifically the most rewarding among equally likely alternatives. We aim at simplicity and hope for truth.

For if there is any truth in the dynamical theory of gases the different molecules in a gas at uniform temperature are moving with very different velocities. Put such a gas into a vessel with two compartments [A and B] and make a small hole in the wall about the right size to let one molecule through. Provide a lid or stopper for this hole and appoint a doorkeeper, very intelligent and exceedingly quick, with microscopic eyes but still an essentially finite being.Whenever he sees a molecule of great velocity coming against the door from A into B he is to let it through, but if the molecule happens to be going slow he is to keep the door shut. He is also to let slow molecules pass from B to A but not fast ones ... In this way the temperature of B may be raised and that of A lowered without any expenditure of work, but only by the intelligent action of a mere guiding agent (like a pointsman on a railway with perfectly acting switches who should send the express along one line and the goods along another).I do not see why even intelligence might not be dispensed with and the thing be made self-acting.Moral The 2nd law of Thermodynamics has the same degree of truth as the statement that if you throw a tumblerful of water into the sea you cannot get the same tumblerful of water out again.

For strictly scientific or technological purposes all this is irrelevant. On a pragmatic view, as on a religious view, theory and concepts are held in faith. On the pragmatic view the only thing that matters is that the theory is efficacious, that it 'works' and that the necessary preliminaries and side issues do not cost too much in time and effort. Beyond that, theory and concepts go to constitute a language in which the scientistic matters at issue can be formulated and discussed.

Fortunately I experienced Max Wertheimer's teaching in Berlin and collaborated for over a decade with Wolfgang Köhler. I need not emphasize my debts to these outstanding personalities. The fundamental ideas of Gestalt theory are the foundation of all our investigations in the field of the will, of affection, and of the personality.

Freudian psychoanalytical theory is a mythology that answers pretty well to Levi-Strauss's descriptions. It brings some kind of order into incoherence; it, too, hangs together, makes sense, leaves no loose ends, and is never (but never) at a loss for explanation. In a state of bewilderment it may therefore bring comfort and relief … give its subject a new and deeper understanding of his own condition and of the nature of his relationship to his fellow men. A mythical structure will be built up around him which makes sense and is believable-in, regardless of whether or not it is true.

From the medical theoretical standpoint, it suffices to deliberate and speculate regarding most illnesses. However, therapeutically, speculation is not adequate, and true and correct knowledge is imperative.

From the point of view of the pure morphologist the recapitulation theory is an instrument of research enabling him to reconstruct probable lines of descent; from the standpoint of the student of development and heredity the fact of recapitulation is a difficult problem whose solution would perhaps give the key to a true understanding of the real nature of heredity.

Generally speaking, geologists seem to have been much more intent on making little worlds of their own, than in examining the crust of that which they inhabit. It would be much more desirable that facts should be placed in the foreground and theories in the distance, than that theories should be brought forward at the expense of facts. So that, in after times, when the speculations of the present day shall have passed away, from a greater accumulation of information, the facts may be readily seized and converted to account.

Good lawyers know that in many cases where the decisions are correct, the reasons that are given to sustain them may be entirely wrong. This is a thousand times more likely to be true in the practice of medicine than in that of the law, and hence the impropriety, not to say the folly, in spending your time in the discussion of medical belief and theories of cure that are more ingenious and seductive than they are profitable.

Here I shall present, without using Analysis [mathematics], the principles and general results of the Théorie, applying them to the most important questions of life, which are indeed, for the most part, only problems in probability. One may even say, strictly speaking, that almost all our knowledge is only probable; and in the small number of things that we are able to know with certainty, in the mathematical sciences themselves, the principal means of arriving at the truth—induction and analogy—are based on probabilities, so that the whole system of human knowledge is tied up with the theory set out in this essay.

His [Thomas Edison] method was inefficient in the extreme, for an immense ground had to be covered to get anything at all unless blind chance intervened and, at first, I was almost a sorry witness of his doings, knowing that just a little theory and calculation would have saved him 90 per cent of the labor. But he had a veritable contempt for book learning and mathematical knowledge, trusting himself entirely to his inventor's instinct and practical American sense. In view of this, the truly prodigious amount of his actual accomplishments is little short of a miracle.

Historical theories are, after all, intellectual apple carts. They are quite likely to be upset. Nor should it be forgotten that they tend to attract, when they gain ascendancy, a fair number of apple-polishers

How strange it would be if the final theory were to be discovered in our lifetimes! The discovery of the final laws of nature will mark a discontinuity in human intellectual history, the sharpest that has occurred since the beginning of modern science in the seventeenth century. Can we now imagine what that would be like?

How then did we come to the “standard model”? And how has it supplanted other theories, like the steady state model? It is a tribute to the essential objectivity of modern astrophysics that this consensus has been brought about, not by shifts in philosophical preference or by the influence of astrophysical mandarins, but by the pressure of empirical data.

How thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.

In 'Mathematical Problems', Lecture at the International Congress of Mathematics, Paris, (8 Aug 1900). Translated by Dr. Maby Winton Newson in Bulletin of the American Mathematical Society (1902), 8, 479. As quoted and cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 94-95. It is reprinted in Jeremy Gray, The Hilbert Challenge (2000), 282.

Hygiene is the corruption of medicine by morality. It is impossible to find a
hygienist who does not debase his theory of the healthful with a theory of the virtuous. ... The aim of medicine is surely not to make men virtuous; it is to safeguard them from the consequences of their vices.

I always love geology. In winter, particularly, it is pleasant to listen to theories about the great mountains one visited in the summer; or about the Flood or volcanoes; about great catastrophes or about blisters; above all about fossils … Everywhere there are hypotheses, but nowhere truths; many workmen, but no experts; priests, but no God. In these circumstances each man can bring his hypothesis like a candle to a burning altar, and on seeing his candle lit declare ‘Smoke for smoke, sir, mine is better than yours’. It is precisely for this reason that I love geology.

I am afraid all we can do is to accept the paradox and try to accommodate ourselves to it, as we have done to so many paradoxes lately in modern physical theories. We shall have to get accustomed to the idea that the change of the quantity R, commonly called the 'radius of the universe', and the evolutionary changes of stars and stellar systems are two different processes, going on side by side without any apparent connection between them. After all the 'universe' is an hypothesis, like the atom, and must be allowed the freedom to have properties and to do things which would be contradictory and impossible for a finite material structure.

I am now convinced that we have recently become possessed of experimental evidence of the discrete or grained nature of matter, which the atomic hypothesis sought in vain for hundreds and thousands of years. The isolation and counting of gaseous ions, on the one hand, which have crowned with success the long and brilliant researches of J.J. Thomson, and, on the other, agreement of the Brownian movement with the requirements of the kinetic hypothesis, established by many investigators and most conclusively by J. Perrin, justify the most cautious scientist in now speaking of the experimental proof of the atomic nature of matter, The atomic hypothesis is thus raised to the position of a scientifically well-founded theory, and can claim a place in a text-book intended for use as an introduction to the present state of our knowledge of General Chemistry.

I am particularly concerned to determine the probability of causes and results, as exhibited in events that occur in large numbers, and to investigate the laws according to which that probability approaches a limit in proportion to the repetition of events. That investigation deserves the attention of mathematicians because of the analysis required. It is primarily there that the approximation of formulas that are functions of large numbers has its most important applications. The investigation will benefit observers in identifying the mean to be chosen among the results of their observations and the probability of the errors still to be apprehended. Lastly, the investigation is one that deserves the attention of philosophers in showing how in the final analysis there is a regularity underlying the very things that seem to us to pertain entirely to chance, and in unveiling the hidden but constant causes on which that regularity depends. It is on the regularity of the main outcomes of events taken in large numbers that various institutions depend, such as annuities, tontines, and insurance policies. Questions about those subjects, as well as about inoculation with vaccine and decisions of electoral assemblies, present no further difficulty in the light of my theory. I limit myself here to resolving the most general of them, but the importance of these concerns in civil life, the moral considerations that complicate them, and the voluminous data that they presuppose require a separate work.

I bet it would have been a lot of fun to work with Einstein. What I really respect about Einstein is his desire to throw aside all conventional modes and just concentrate on what seems to be the closest we can get to an accurate theory of nature.

I can assure you, reader, that in a very few hours, even during the first day, you will learn more natural philosophy about things contained in this book, than you could learn in fifty years by reading the theories and opinions of the ancient philosophers. Enemies of science will scoff at the astrologers: saying, where is the ladder on which they have climbed to heaven, to know the foundation of the stars? But in this respect I am exempt from such scoffing; for in proving my written reason, I satisfy sight, hearing, and touch: for this reason, defamers will have no power over me: as you will see when you come to see me in my little Academy.

I can well appreciate, Holy Father, that as soon as certain people realise that in these books which I have written about the Revolutions of the spheres of the universe I attribute certain motions to the globe of the Earth, they will at once clamour for me to be hooted off the stage with such an opinion.

I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.

I first met J. Robert Oppenheimer on October 8, 1942, at Berkeley, Calif. There we discussed the theoretical research studies he was engaged in with respect to the physics of the bomb. Our discussions confirmed my previous belief that we should bring all of the widely scattered theoretical work together. … He expressed complete agreement, and it was then that the idea of the prompt establishment of a Los Alamos was conceived.”

I had made considerable advance ... in calculations on my favourite numerical lunar theory, when I discovered that, under the heavy pressure of unusual matters (two transits of Venus and some eclipses) I had committed a grievous error in the first stage of giving numerical value to my theory. My spirit in the work was broken, and I have never heartily proceeded with it since.[Concerning his calculations on the orbital motion of the Moon.]

I have a peculiar theory about radium, and I believe it is the correct one. I believe that there is some mysterious ray pervading the universe that is fluorescing to it. In other words, that all its energy is not self-constructed but that there is a mysterious something in the atmosphere that scientists have not found that is drawing out those infinitesimal atoms and distributing them forcefully and indestructibly.

I have been scientifically studying the traits and dispositions of the “lower animals” (so-called,) and contrasting them with the traits and dispositions of man. I find the result profoundly humiliating to me. For it obliges me to renounce my allegiance to the Darwinian theory of the Ascent of Man from the Lower Animals; since it now seems plain to me that that theory ought to be vacated in favor of a new and truer one, this new and truer one to be named the Descent of Man from the Higher Animals.

Alleged comment to the secretary of the Netherlands embassy, seated beside him at a National Academy of Sciences annual awards ceremony (1921), after listening to lengthy formal speeches. As quoted in Ronald W. Clark, Einstein: The Life and Times (1971), 389.

I have learnt that all our theories are not Truth itself, but resting places or stages on the way to the conquest of Truth, and that we must be contented to have obtained for the strivers after Truth such a resting place which, if it is on a mountain, permits us to view the provinces already won and those still to be conquered.

I have no doubt that certain learned men, now that the novelty of the hypotheses in this work has been widely reported—for it establishes that the Earth moves, and indeed that the Sun is motionless in the middle of the universe—are extremely shocked, and think that the scholarly disciplines, rightly established once and for all, should not be upset. But if they are willing to judge the matter thoroughly, they will find that the author of this work has committed nothing which deserves censure. For it is proper for an astronomer to establish a record of the motions of the heavens with diligent and skilful observations, and then to think out and construct laws for them, or rather hypotheses, whatever their nature may be, since the true laws cannot be reached by the use of reason; and from those assumptions the motions can be correctly calculated, both for the future and for the past. Our author has shown himself outstandingly skilful in both these respects. Nor is it necessary that these hypotheses should be true, nor indeed even probable, but it is sufficient if they merely produce calculations which agree with the observations... For it is clear enough that this subject is completely and simply ignorant of the laws which produce apparently irregular motions. And if it does work out any laws—as certainly it does work out very many—it does not do so in any way with the aim of persuading anyone that they are valid, but only to provide a correct basis for calculation. Since different hypotheses are sometimes available to explain one and the same motion (for instance eccentricity or an epicycle for the motion of the Sun) an astronomer will prefer to seize on the one which is easiest to grasp; a philosopher will perhaps look more for probability; but neither will grasp or convey anything certain, unless it has been divinely revealed to him. Let us therefore allow these new hypotheses also to become known beside the older, which are no more probable, especially since they are remarkable and easy; and let them bring with them the vast treasury of highly learned observations. And let no one expect from astronomy, as far as hypotheses are concerned, anything certain, since it cannot produce any such thing, in case if he seizes on things constructed for another other purpose as true, he departs from this discipline more foolish than he came to it.Assumed by contemporary readers to be written by Copernicus himself, this preface suggested the earth's motion was merely a mathematical device and not to be taken seriously.

I have no trouble publishing in Soviet astrophysical journals, but my work is unacceptable to the American astrophysical journals.[Referring to the trouble he had with the peer reviewers of Anglo-American astrophysical journals because his ideas often conflicted with the generally accepted or “standard"” theories.]

I learnt to distrust all physical concepts as the basis for a theory. Instead one should put one's trust in a mathematical scheme, even if the scheme does not appear at first sight to be connected with physics. One should concentrate on getting interesting mathematics.

I noticed affixed to a laboratory door the following words: “Les théories passent. Le Grenouille reste. [The theories pass. The frog remains.] &mdashJean Rostand, Carnets d’un biologiste.” There is a risk that in the less severe discipline of criticism the result may turn out to be different; the theories will remain but the frog may disappear.

I once knew an otherwise excellent teacher who compelled his students to perform all their demonstrations with incorrect figures, on the theory that it was the logical connection of the concepts, not the figure, that was essential.

I shall explain a System of the World differing in many particulars from any yet known, answering in all things to the common Rules of Mechanical Motions: This depends upon three Suppositions. First, That all Cœlestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from them, as we may observe the Earth to do, but that they do also attract all the other Cœlestial bodies that are within the sphere of their activity; and consequently that not only the Sun and Moon have an influence upon the body and motion the Earth, and the Earth upon them, but that Mercury also Venus, Mars, Saturn and Jupiter by their attractive powers, have a considerable influence upon its motion in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into a Motion, describing a Circle, Ellipse, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centers. Now what these several degrees are I have not yet experimentally verified; but it is a notion, which if fully prosecuted as it ought to be, will mightily assist the Astronomer to reduce all the Cœlestial Motions to a certain rule, which I doubt will never be done true without it. He that understands the nature of the Circular Pendulum and Circular Motion, will easily understand the whole ground of this Principle, and will know where to find direction in Nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this Inquiry, and are not wanting of Industry for observing and calculating, wishing heartily such may be found, having myself many other things in hand which I would first compleat and therefore cannot so well attend it. But this I durst promise the Undertaker, that he will find all the Great Motions of the World to be influenced by this Principle, and that the true understanding thereof will be the true perfection of Astronomy.

I should like to call the number of atom groups, with which an elementary atom coordinates … to form a complex radical, the coordination number of the atom in question … We must differentiate between valence number and coordination number. The valence number indicates the maximum number of monovalent atoms which can be bound directly to the atom in question without the participation of other elementary atoms … Perhaps this concept [of coordination number] is destined to serve as a basis for the theory of the constitution of inorganic compounds, just as valence theory formed the basis for the constitutional theory of carbon compounds.

I therefore took this opportunity and also began to consider the possibility that the Earth moved. Although it seemed an absurd opinion, nevertheless, because I knew that others before me had been granted the liberty of imagining whatever circles they wished to represent the phenomena of the stars, I thought that I likewise would readily be allowed to test whether, by assuming some motion of the Earth's, more dependable representations than theirs could be found for the revolutions of the heavenly spheres.

I think a strong claim can be made that the process of scientific discovery may be regarded as a form of art. This is best seen in the theoretical aspects of Physical Science. The mathematical theorist builds up on certain assumptions and according to well understood logical rules, step by step, a stately edifice, while his imaginative power brings out clearly the hidden relations between its parts. A well constructed theory is in some respects undoubtedly an artistic production. A fine example is the famous Kinetic Theory of Maxwell. ... The theory of relativity by Einstein, quite apart from any question of its validity, cannot but be regarded as a magnificent work of art.Responding to the toast, 'Science!' at the Royal Academy of the Arts in 1932.)

I was pretty good in science. But again, because of the small budget, in science class we couldn't do experiments in order to prove theories. We just believed everything. Actually I think that class was call Religion. Religion was always an easy class. All you had to do was suspend the logic and reasoning you were taught in all the other classes.

I was there when Abbe Georges Lemaître first proposed this [Big Bang] theory. ... There is no rational reason to doubt that the universe has existed indefinitely, for an infinite time. .... It is only myth that attempts to say how the universe came to be, either four thousand or twenty billion years ago.[Expressing his belief that the Big Bang is a myth devised to explain creation. He said he heard Lemaître (who was, at the time both a member of the Catholic hierarchy and an accomplished scientist) say in private that this theory was a way to reconcile science with St. Thomas Aquinas' theological dictum of creatio ex nihilo—creation out of nothing.]

I will simply express my strong belief, that that point of self-education which consists in teaching the mind to resist its desires and inclinations, until they are proved to be right, is the most important of all, not only in things of natural philosophy, but in every department of dally life.

As reported by Heisenberg describing Schrödinger’s time spent debating with Bohr in Copenhagen (Sep 1926). In Werner Heisenberg, Physics and Beyond: Encounters and Conversations (1971), 75. As cited in John Gribbin, Erwin Schrodinger and the Quantum Revolution.

If he [Thomas Edison] had a needle to find in a haystack, he would not stop to reason where it was most likely to be, but would proceed at once with the feverish diligence of a bee, to examine straw after straw until he found the object of his search. … [J]ust a little theory and calculation would have saved him ninety percent of his labor.

If history is any guide at all, it seems to me to suggest that there is a final theory. In this century we have seen a convergence of the arrows of explanation, like the convergence of meridians toward the North Pole.

If in a discussion of many matters … we are not able to give perfectly exact and self-consistent accounts, do not be surprised: rather we would be content if we provide accounts that are second to none in probability.

If this plane were to crash, we could get a new start on this quasar problem.Said to colleagues, dramatically cupping his hand over his brow, shortly after the take-off of a propeller plane leaving Austin, Texas, after the Second Texas Symposium for Relativistic Astrophysics in Dec 1964. Various different theories had been presented at the conference. The flight passengers included many of the major scientists in quasar research, including Margaret and Geoffrey Burbridge, Subrahmanyan Chandrasekhar, John Wheeler and Maarten Schmidt.

If we do discover a complete theory, it should be in time understandable in broad principle by everyone ... Then we shall all, philosophers, scientists and just ordinary people, be able to take part in the discussion of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason—for then we would know the mind of God.

In 1975, ... [speaking with Shiing Shen Chern], I told him I had finally learned ... the beauty of fiber-bundle theory and the profound Chern-Weil theorem. I said I found it amazing that gauge fields are exactly connections on fiber bundles, which the mathematicians developed without reference to the physical world. I added, “this is both thrilling and puzzling, since you mathematicians dreamed up these concepts out of nowhere.” He immediately protested: “No, no. These concepts were not dreamed up. They were natural and real.”

In 'Einstein's Impact on Theoretical Physics', collected in Jong-Ping Hsu, Leonard Hsu (eds.), JingShin Theoretical Physics Symposium in Honor of Professor Ta-You Wu (1998), 70. Reprinted from Physics Today (Jun 1980), 49. The article was adapted from a talk given at the Second Marcel Grossman meeting, held in Trieste, Italy (Jul 1979), in honor of the 100th anniversary of the birth of Albert Einstein.

Attributed. Although widely seen, a reliable source is never cited. If you know a primary print source, please contact Webmaster. Occasionally also seen attributed to Yogi Berra, Chuck Reid, Grant Gainey or Jerry Percell. The earliest example found by Webmaster is in Walter J. Savitch, An Introduction to the Art and Science of Programming (1986), where it is merely attributed as "Remark overheard at a computer science conference."

In a sense, of course, probability theory in the form of the simple laws of chance is the key to the analysis of warfare;… My own experience of actual operational research work, has however, shown that its is generally possible to avoid using anything more sophisticated. … In fact the wise operational research worker attempts to concentrate his efforts in finding results which are so obvious as not to need elaborate statistical methods to demonstrate their truth. In this sense advanced probability theory is something one has to know about in order to avoid having to use it.

In an enterprise such as the building of the atomic bomb the difference between ideas, hopes, suggestions and theoretical calculations, and solid numbers based on measurement, is paramount. All the committees, the politicking and the plans would have come to naught if a few unpredictable nuclear cross sections had been different from what they are by a factor of two.

In chemistry, our theories are crutches; to show that they are valid, they must be used to walk... A theory established with the help of twenty facts must explain thirty, and lead to the discovery of ten more.

In fact, Gentlemen, no geometry without arithmetic, no mechanics without geometry... you cannot count upon success, if your mind is not sufficiently exercised on the forms and demonstrations of geometry, on the theories and calculations of arithmetic ... In a word, the theory of proportions is for industrial teaching, what algebra is for the most elevated mathematical teaching.

In general, art has preceded science. Men have executed great, and curious, and beautiful works before they had a scientific insight into the principles on which the success of their labours was founded. There were good artificers in brass and iron before the principles of the chemistry of metals were known; there was wine among men before there was a philosophy of vinous fermentation; there were mighty masses raised into the air, cyclopean walls and cromlechs, obelisks and pyramids—probably gigantic Doric pillars and entablatures—before there was a theory of the mechanical powers. … Art was the mother of Science.

Lecture (26 Nov 1851), to the London Society of Arts, 'The General Bearing of the Great Exhibition on the Progress of Art and Science', collected in Lectures on the Results of the Great Exhibition of 1851' (1852), 7-8.

In less than eight years “The Origin of Species” has produced conviction in the minds of a majority of the most eminent living men of science. New facts, new problems, new difficulties as they arise are accepted, solved, or removed by this theory; and its principles are illustrated by the progress and conclusions of every well established branch of human knowledge.

From a review of four books on the subject 'Mimicry, and Other Protective Resemblances Among Animals', in The Westminster Review (Jul 1867), 88, 1. Wallace is identified as the author in the article as reprinted in William Beebe, The Book of Naturalists: An Anthology of the Best Natural History (1988), 108.

In my own view, some advice about what should be known, about what technical education should be acquired, about the intense motivation needed to succeed, and about the carelessness and inclination toward bias that must be avoided is far more useful than all the rules and warnings of theoretical logic.

In our day grand generalizations have been reached. The theory of the origin of species is but one of them. Another, of still wider grasp and more radical significance, is the doctrine of the Conservation of Energy, the ultimate philosophical issues of which are as yet but dimly seem-that doctrine which 'binds nature fast in fate' to an extent not hitherto recognized, exacting from every antecedent its equivalent consequent, and bringing vital as well as physical phenomena under the dominion of that law of causal connexion which, so far as the human understanding has yet pierced, asserts itself everywhere in nature.

'Address Delivered Before The British Association Assembled at Belfast', (19 Aug 1874). Fragments of Science for Unscientific People: A Series of Detached Essays, Lectures, and Reviews (1892), Vol. 2, 1801.

In point of fact, no conclusive disproof of a theory can ever be produced; for it is always possible to say that the experimental results are not reliable or that the discrepancies which are asserted to exist between the experimental results and the theory are only apparent and that they will disappear with the advance of our understanding. If you insist on strict proof (or strict disproof) in the empirical sciences, you will never benefit from experience, and never learn from it how wrong you are.

In science 'fact' can only mean 'confirmed to such a degree that it would be perverse to withhold provisional assent'. I suppose that apples might start to rise tomorrow, but the possibility does not merit equal time in physics classrooms.

In scientific study, or, as I prefer to phrase it, in creative scholarship, the truth is the single end sought; all yields to that. The truth is supreme, not only in the vague mystical sense in which that expression has come to be a platitude, but in a special, definite, concrete sense. Facts and the immediate and necessary inductions from facts displace all pre-conceptions, all deductions from general principles, all favourite theories. Previous mental constructions are bowled over as childish play-structures by facts as they come rolling into the mind. The dearest doctrines, the most fascinating hypotheses, the most cherished creations of the reason and of the imagination perish from a mind thoroughly inspired with the scientific spirit in the presence of incompatible facts. Previous intellectual affections are crushed without hesitation and without remorse. Facts are placed before reasonings and before ideals, even though the reasonings and the ideals be more beautiful, be seemingly more lofty, be seemingly better, be seemingly truer. The seemingly absurd and the seemingly impossible are sometimes true. The scientific disposition is to accept facts upon evidence, however absurd they may appear to our pre-conceptions.

In the expressions we adopt to prescribe physical phenomena we necessarily hover between two extremes. We either have to choose a word which implies more than we can prove, or we have to use vague and general terms which hide the essential point, instead of bringing it out. The history of electrical theories furnishes a good example.

In the year 1666 he retired again from Cambridge... to his mother in Lincolnshire & whilst he was musing in a garden it came into his thought that the power of gravity (wch brought an apple from the tree to the ground) was not limited to a certain distance from the earth but that this power must extend much farther than was usually thought. Why not as high as the moon said he to himself & if so that must influence her motion & perhaps retain her in her orbit, whereupon he fell a calculating what would be the effect of that supposition but being absent from books & taking the common estimate in use among Geographers & our seamen before Norwood had measured the earth, that 60 English miles were contained in one degree of latitude on the surface of the Earth his computation did not agree with his theory & inclined him then to entertain a notion that together with the force of gravity there might be a mixture of that force wch the moon would have if it was carried along in a vortex.[The earliest account of Newton, gravity and an apple.]

In the year 1902 (while I was attempting to explain to an elementary class in chemistry some of the ideas involved in the periodic law) becoming interested in the new theory of the electron, and combining this idea with those which are implied in the periodic classification, I formed an idea of the inner structure of the atom which, although it contained certain crudities, I have ever since regarded as representing essentially the arrangement of electrons in the atom ... In accordance with the idea of Mendeleef, that hydrogen is the first member of a full period, I erroneously assumed helium to have a shell of eight electrons. Regarding the disposition in the positive charge which balanced the electrons in the neutral atom, my ideas were very vague; I believed I inclined at that time toward the idea that the positive charge was also made up of discrete particles, the localization of which determined the localization of the electrons.

In theory one is aware that the earth revolves but in practice one does not perceive it, the ground on which one treads seems not to move, and one can live undisturbed. So it is with Time in one's life. (1918)

In these researches I followed the principles of the experimental method that we have established, i.e., that, in presence of a well-noted, new fact which contradicts a theory, instead of keeping the theory and abandoning the fact, I should keep and study the fact, and I hastened to give up the theory.

In-depth studies have an influence on general ideas, whereas theories, in turn, in order to maintain themselves, push their spectators to search for new evidence. The mind's activity that is maintained by the debates about these works, is probably the source of the greatest joys given to man to experience on Earth.

Indeed, the most important part of engineering work—and also of other scientific work—is the determination of the method of attacking the problem, whatever it may be, whether an experimental investigation, or a theoretical calculation. … It is by the choice of a suitable method of attack, that intricate problems are reduced to simple phenomena, and then easily solved.

Is evolution a theory, a system or a hypothesis? It is much more: it is a general condition to which all theories, all hypotheses, all systems must bow and which they must satisfy henceforth if they are to be thinkable and true. Evolution is a light illuminating all facts, a curve that all lines must follow. ... The consciousness of each of us is evolution looking at itself and reflecting upon itself....Man is not the center of the universe as once we thought in our simplicity, but something much more wonderful—the arrow pointing the way to the final unification of the world in terms of life. Man alone constitutes the last-born, the freshest, the most complicated, the most subtle of all the successive layers of life. ... The universe has always been in motion and at this moment continues to be in motion. But will it still be in motion tomorrow? ... What makes the world in which we live specifically modern is our discovery in it and around it of evolution. ... Thus in all probability, between our modern earth and the ultimate earth, there stretches an immense period, characterized not by a slowing-down but a speeding up and by the definitive florescence of the forces of evolution along the line of the human shoot.

It appears that anything you say about the way that theory and experiment may interact is likely to be correct, and anything you say about the way that theory and experiment must interact is likely to be wrong.

It does appear that on the whole a physicist… tries to reduce his theory at all times to as few parameters as possible and is inclined to feel that a theory is a “respectable” one, though by no means necessarily correct, if in principle it does offer reasonably specific means for its possible refutation. Moreover the physicist will generally arouse the irritation amongst fellow physicists if he is not prepared to abandon his theory when it clashes with subsequent experiments. On the other hand it would appear that the chemist regards theories—or perhaps better his theories (!) —as far less sacrosanct, and perhaps in extreme cases is prepared to modify them continually as each bit of new experimental evidence comes in.

It has been said by a distinguished philosopher that England is “usually the last to enter into the general movement of the European mind.” The author of the remark probably meant to assert that a man or a system may have become famous on the continent, while we are almost ignorant of the name of the man and the claims of his system. Perhaps, however, a wider range might be given to the assertion. An exploded theory or a disadvantageous practice, like a rebel or a patriot in distress, seeks refuge on our shores to spend its last days in comfort if not in splendour.

It has often been said that, to make discoveries, one must be ignorant. This opinion, mistaken in itself, nevertheless conceals a truth. It means that it is better to know nothing than to keep in mind fixed ideas based on theories whose confirmation we constantly seek, neglecting meanwhile everything that fails to agree with them.

It is a vulgar belief that our astronomical knowledge dates only from the recent century when it was rescued from the monks who imprisoned Galileo; but Hipparchus … who among other achievements discovered the precession of the eqinoxes, ranks with the Newtons and the Keplers; and Copernicus, the modern father of our celestial science, avows himself, in his famous work, as only the champion of Pythagoras, whose system he enforces and illustrates. Even the most modish schemes of the day on the origin of things, which captivate as much by their novelty as their truth, may find their precursors in ancient sages, and after a careful analysis of the blended elements of imagination and induction which charaterise the new theories, they will be found mainly to rest on the atom of Epicurus and the monad of Thales. Scientific, like spiritual truth, has ever from the beginning been descending from heaven to man.

It is an old saying, abundantly justified, that where sciences meet there growth occurs. It is true moreover to say that in scientific borderlands not only are facts gathered that [are] often new in kind, but it is in these regions that wholly new concepts arise. It is my own faith that just as the older biology from its faithful studies of external forms provided a new concept in the doctrine of evolution, so the new biology is yet fated to furnish entirely new fundamental concepts of science, at which physics and chemistry when concerned with the non-living alone could never arrive.

It is customary to connect Medicine with Botany, yet scientific treatment demands that we should consider each separately. For the fact is that in every art, theory must be disconnected and separated from practice, and the two must be dealt with singly and individually in their proper order before they are united. And for that reason, in order that Botany, which is, as it were, a special branch of Natural Philosophy [Physica], may form a unit by itself before it can be brought into connection with other sciences, it must be divided and unyoked from Medicine.

It is difficult even to attach a precise meaning to the term “scientific truth.” So different is the meaning of the word “truth” according to whether we are dealing with a fact of experience, a mathematical proposition or a scientific theory. “Religious truth” conveys nothing clear to me at all.

It is easy to make out three areas where scientists will be concentrating their efforts in the coming decades. One is in physics, where leading theorists are striving, with the help of experimentalists, to devise a single mathematical theory that embraces all the basic phenomena of matter and energy. The other two are in biology. Biologists—and the rest of us too—would like to know how the brain works and how a single cell, the fertilized egg cell, develops into an entire organism

It is easy to obtain confirmations, or verifications, for nearly every theory—if we look for confirmations. Confirmations should count only if they are the result of risky predictions... A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice. Every genuine test of a theory is an attempt to falsify it, or refute it.

It is going to be necessary that everything that happens in a finite volume of space and time would have to be analyzable with a finite number of logical operations. The present theory of physics is not that way, apparently. It allows space to go down into infinitesimal distances, wavelengths to get infinitely great, terms to be summed in infinite order, and so forth; and therefore, if this proposition [that physics is computer-simulatable] is right, physical law is wrong.

It is in scientific honesty that I endorse the presentation of alternative theories for the origin of the universe, life and man in the science classroom. It would be an error to overlook the possibility that the universe was planned rather than happening by chance.

It is more important to have beauty in one's equations than to have them fit experiment... It seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory.

'Falsification and the Methodology of Scientific Research Programmes', in I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science, London 1965 (1970), Vol. 4, 130.

It is often held that scientific hypotheses are constructed, and are to be constructed, only after a detailed weighing of all possible evidence bearing on the matter, and that then and only then may one consider, and still only tentatively, any hypotheses. This traditional view however, is largely incorrect, for not only is it absurdly impossible of application, but it is contradicted by the history of the development of any scientific theory. What happens in practice is that by intuitive insight, or other inexplicable inspiration, the theorist decides that certain features seem to him more important than others and capable of explanation by certain hypotheses. Then basing his study on these hypotheses the attempt is made to deduce their consequences. The successful pioneer of theoretical science is he whose intuitions yield hypotheses on which satisfactory theories can be built, and conversely for the unsuccessful (as judged from a purely scientific standpoint). Co-author with British astronomer, Raymond Arthur Lyttleton (1911-95).

It is scientists, not sceptics, who are most willing to consider explanations that conflict with their own. And far from quashing dissent, it is the scientists, not the sceptics, who do most to acknowledge gaps in their studies and point out the limitations of their data—which is where sceptics get much of the mud they fling at the scientists. By contrast, the [sceptics] are not trying to build a theory of anything. They have set the bar much lower, and are happy muddying the waters.

It is … a sign of the times—though our brothers of physics and chemistry may smile to hear me say so—that biology is now a science in which theories can be devised: theories which lead to predictions and predictions which sometimes turn out to be correct. These facts confirm me in a belief I hold most passionately—that biology is the heir of all the sciences.

It must be conceded that a theory has an important advantage if its basic concepts and fundamental hypotheses are 'close to experience,' and greater confidence in such a theory is certainly justified. There is less danger of going completely astray, particularly since it takes so much less time and effort to disprove such theories by experience. Yet more and more, as the depth of our knowledge increases, we must give up this advantage in our quest for logical simplicity in the foundations of physical theory...

It seems sensible to discard all hope of observing hitherto unobservable quantities, such as the position and period of the electron... Instead it seems more reasonable to try to establish a theoretical quantum mechanics, analogous to classical mechanics, but in which only relations between observable quantities occur.

It seems to me, he says, that the test of “Do we or not understand a particular subject in physics?” is, “Can we make a mechanical model of it?” I have an immense admiration for Maxwell’s model of electromagnetic induction. He makes a model that does all the wonderful things that electricity docs in inducing currents, etc., and there can be no doubt that a mechanical model of that kind is immensely instructive and is a step towards a definite mechanical theory of electromagnetism.

From stenographic report by A.S. Hathaway of the Lecture 20 Kelvin presented at Johns Hopkins University, Baltimore, on 'Molecular Dynamics and the Wave Theory of Light' (1884), 132. (Hathaway was a Mathematics fellow there.) This remark is not included in the first typeset publication—a revised version, printed twenty years later, in 1904, as Lord Kelvin’s Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light. The original notes were reproduced by the “papyrograph” process. They are excerpted in Pierre Maurice Marie Duhem, Essays in the History and Philosophy of Science (1996), 54-55.

It surely can be no offence to state, that the progress of science has led to new views, and that the consequences that can be deduced from the knowledge of a hundred facts may be very different from those deducible from five. It is also possible that the facts first known may be the exceptions to a rule and not the rule itself, and generalisations from these first-known facts, though useful at the time, may be highly mischievous, and impede the progress of the science if retained when it has made some advance.

Just now nuclear physicists are writing a great deal about hypothetical particles called neutrinos supposed to account for certain peculiar facts observed in ß-ray disintegration. We can perhaps best describe the neutrinos as little bits of spin-energy that have got detached. I am not much impressed by the neutrino theory. In an ordinary way I might say that I do not believe in neutrinos... But I have to reflect that a physicist may be an artist, and you never know where you are with artists. My old-fashioned kind of disbelief in neutrinos is scarcely enough. Dare I say that experimental physicists will not have sufficient ingenuity to make neutrinos? Whatever I may think, I am not going to be lured into a wager against the skill of experimenters under the impression that it is a wager against the truth of a theory. If they succeed in making neutrinos, perhaps even in developing industrial applications of them, I suppose I shall have to believe—though I may feel that they have not been playing quite fair.

Later scientific theories are better than earlier ones for solving puzzles in the often quite different environments to which they are applied. That is not a relativist's position, and it displays the sense in which I am a convinced believer in scientific progress.

Let us award a just, a brilliant homage to those rare men whom nature has endowed with the precious privilege of arranging a thousand isolated facts, of making seductive theories spring from them; but let us not forget to state, that the scythe of the reaper had cut the stalks before one had thought of uniting them into sheaves!

Let us now recapitulate all that has been said, and let us conclude that by hermetically sealing the vials, one is not always sure to prevent the birth of the animals in the infusions, boiled or done at room temperature, if the air inside has not felt the ravages of fire. If, on the contrary, this air has been powerfully heated, it will never allow the animals to be born, unless new air penetrates from outside into the vials. This means that it is indispensable for the production of the animals that they be provided with air which has not felt the action of fire. And as it would not be easy to prove that there were no tiny eggs disseminated and floating in the volume of air that the vials contain, it seems to me that suspicion regarding these eggs continues, and that trial by fire has not entirely done away with fears of their existence in the infusions. The partisans of the theory of ovaries will always have these fears and will not easily suffer anyone's undertaking to demolish them.

Mathematicians deal with possible worlds, with an infinite number of logically consistent systems. Observers explore the one particular world we inhabit. Between the two stands the theorist. He studies possible worlds but only those which are compatible with the information furnished by observers. In other words, theory attempts to segregate the minimum number of possible worlds which must include the actual world we inhabit. Then the observer, with new factual information, attempts to reduce the list further. And so it goes, observation and theory advancing together toward the common goal of science, knowledge of the structure and observation of the universe.

Men who believe too firmly in their theories, do not believe enough in the theories of others. So … these despisers of their fellows … make experiments only to destroy a theory, instead of to seek the truth.

Men who have excessive faith in their theories or ideas are not only ill prepared for making discoveries; they also make very poor observations. Of necessity, they observe with a preconceived idea, and when they devise an experiment, they can see, in its results,only a confirmation of their theory. In this way they distort observation and often neglect very important facts because they do not further their aim.

Men who have excessive faith in their theories … make poor observations, because they choose among the results of their experiments only what suits their object, neglecting whatever is unrelated to it and carefully setting aside everything which might tend toward the idea they wish to combat

Modern theories did not arise from revolutionary ideas which have been, so to speak, introduced into the exact sciences from without. On the contrary they have forced their way into research which was attempting consistently to carry out the programme of classical physics—they arise out of its very nature. It is for this reason that the beginnings of modern physics cannot be compared with the great upheavals of previous periods like the achievements of Copernicus. Copernicus’s idea was much more an import from outside into the concepts of the science of his time, and therefore caused far more telling changes in science than the ideas of modern physics are creating to-day.

MOLECULE, n. The ultimate, indivisible unit of matter. It is distinguished from the corpuscle, also the ultimate, indivisible unit of matter, by a closer resemblance to the atom, also the ultimate, indivisible unit of matter. Three great scientific theories of the structure of the universe are the molecular, the corpuscular and the atomic. A fourth affirms, with Haeckel, the condensation or precipitation of matter from ether—whose existence is proved by the condensation or precipitation. The present trend of scientific thought is toward the theory of ions. The ion differs from the molecule, the corpuscle and the atom in that it is an ion. A fifth theory is held by idiots, but it is doubtful if they know any more about the matter than the others.

Morphological information has provided the greatest single source of data in the formulation and development of the theory of evolution and that even now, when the preponderance of work is experimental, the basis for interpretation in many areas of study remains the form and relationships of structures.

The Evolution of Physics: The Growth of Ideas from the Early Concepts to Relativity and Quanta (1938), 29. Infeld was a Polish physicist (1898-1968).

Most people like to believe something is or is not true. Great scientists tolerate ambiguity very well. They believe the theory enough to go ahead; they doubt it enough to notice the errors and faults so they can step forward and create the new replacement theory. If you believe too much you’ll never notice the flaws; if you doubt too much you won’t get started. It requires a lovely balance.

Mr Hooke sent, in his next letter [to Sir Isaac Newton] the whole of his Hypothesis, scil that the gravitation was reciprocall to the square of the distance: ... This is the greatest Discovery in Nature that ever was since the World's Creation. It was never so much as hinted by any man before. I wish he had writt plainer, and afforded a little more paper.

Mr Justus Liebig is no doubt a very clever gentleman and a most profound chemist, but in our opinion he knows as much of agriculture as the horse that ploughs the ground, and there is not an old man that stands between the stilts of a plough in Virginia, that cannot tell him of facts totally at variance with his finest spun theories.

Much of the geographical work of the past hundred years... has either explicitly or implicitly taken its inspiration from biology, and in particular Darwin. Many of the original Darwinians, such as Hooker, Wallace, Huxley, Bates, and Darwin himself, were actively concerned with geographical exploration, and it was largely facts of geographical distribution in a spatial setting which provided Darwin with the germ of his theory.

My theory of electrical forces is that they are called into play in insulating media by slight electric displacements, which put certain small portions of the medium into a state of distortion which, being resisted by the elasticity of the medium, produces an electromotive force ... I suppose the elasticity of the sphere to react on the electrical matter surrounding it, and press it downwards.From the determination by Kohlrausch and Weber of the numerical relation between the statical and magnetic effects of electricity, I have determined the elasticity of the medium in air, and assuming that it is the same with the luminiferous ether I have determined the velocity of propagation of transverse vibrations.The result is193088 miles per second(deduced from electrical & magnetic experiments).Fizeau has determined the velocity of light= 193118 miles per secondby direct experiment.This coincidence is not merely numerical. I worked out the formulae in the country, before seeing Webers [sic] number, which is in millimetres, and I think we have now strong reason to believe, whether my theory is a fact or not, that the luminiferous and the electromagnetic medium are one.

My view, the skeptical one, holds that we may be as far away from an understanding of elementary particles as Newton's successors were from quantum mechanics. Like them, we have two tremendous tasks ahead of us. One is to study and explore the mathematics of the existing theories. The existing quantum field-theories may or may not be correct, but they certainly conceal mathematical depths which will take the genius of an Euler or a Hamilton to plumb. Our second task is to press on with the exploration of the wide range of physical phenomena of which the existing theories take no account. This means pressing on with experiments in the fashionable area of particle physics. Outstanding among the areas of physics which have been left out of recent theories of elementary particles are gravitation and cosmology

Nature is disordered, powerful and chaotic, and through fear of the chaos we impose system on it. We abhor complexity, and seek to simplify things whenever we can by whatever means we have at hand. We need to have an overall explanation of what the universe is and how it functions. In order to achieve this overall view we develop explanatory theories which will give structure to natural phenomena: we classify nature into a coherent system which appears to do what we say it does.

'Falsification and the Methodology of Scientific Research Programmes', in I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge: Proceedings of the International Colloquium in the Philosophy of Science, London 1965 (1970), Vol. 4, 116.

No matter how we twist and turn we shall always come back to the cell. The eternal merit of Schwann does not lie in his cell theory that has occupied the foreground for so long, and perhaps will soon be given up, but in his description of the development of the various tissues, and in his demonstration that this development (hence all physiological activity) is in the end traceable back to the cell. Now if pathology is nothing but physiology with obstacles, and diseased life nothing but healthy life interfered with by all manner of external and internal influences then pathology too must be referred back to the cell.

No one has yet been found so firm of mind and purpose as resolutely to compel himself to sweep away all theories and common notions, and to apply the understanding, thus made fair and even, to a fresh examination of particulars. Thus it happens that human knowledge, as we have it, is a mere medley and ill-digested mass, made up of much credulity and much accident, and also of the childish notions which we at first imbibed.

No theory ever agrees with all the facts in its domain, yet it is not always the theory that is to blame. Facts are constituted by older ideologies, and a clash between facts and theories may be proof of progress. It is also a first step in our attempt to find the principles implicit in familiar observational notions.

Nothing in physics seems so hopeful to as the idea that it is possible for a theory to have a high degree of symmetry was hidden from us in everyday life. The physicist's task is to find this deeper symmetry.

Now that we locate them [genes] in the chromosomes are we justified in regarding them as material units; as chemical bodies of a higher order than molecules? Frankly, these are questions with which the working geneticist has not much concern himself, except now and then to speculate as to the nature of the postulated elements. There is no consensus of opinion amongst geneticists as to what the genes are—whether they are real or purely fictitious—because at the level at which the genetic experiments lie, it does not make the slightest difference whether the gene is a hypothetical unit, or whether the gene is a material particle. In either case the unit is associated with a specific chromosome, and can be localized there by purely genetic analysis. Hence, if the gene is a material unit, it is a piece of chromosome; if it is a fictitious unit, it must be referred to a definite location in a chromosome—the same place as on the other hypothesis. Therefore, it makes no difference in the actual work in genetics which point of view is taken. Between the characters that are used by the geneticist and the genes that his theory postulates lies the whole field of embryonic development.

Now, in the development of our knowledge of the workings of Nature out of the tremendously complex assemblage of phenomena presented to the scientific inquirer, mathematics plays in some respects a very limited, in others a very important part. As regards the limitations, it is merely necessary to refer to the sciences connected with living matter, and to the ologies generally, to see that the facts and their connections are too indistinctly known to render mathematical analysis practicable, to say nothing of the complexity.

Observation is so wide awake, and facts are being so rapidly added to the sum of human experience, that it appears as if the theorizer would always be in arrears, and were doomed forever to arrive at imperfect conclusion; but the power to perceive a law is equally rare in all ages of the world, and depends but little on the number of facts observed.

Of all regions of the earth none invites speculation more than that which lies beneath our feet, and in none is speculation more dangerous; yet, apart from speculation, it is little that we can say regarding the constitution of the interior of the earth. We know, with sufficient accuracy for most purposes, its size and shape: we know that its mean density is about 5½ times that of water, that the density must increase towards the centre, and that the temperature must be high, but beyond these facts little can be said to be known. Many theories of the earth have been propounded at different times: the central substance of the earth has been supposed to be fiery, fluid, solid, and gaseous in turn, till geologists have turned in despair from the subject, and become inclined to confine their attention to the outermost crust of the earth, leaving its centre as a playground for mathematicians.

On one occasion when [William] Smart found him engrossed with his fundamental theory, he asked Eddington how many people he thought would understand what he was writing—after a pause came the reply, 'Perhaps seven.'

On the whole, I cannot help saying that it appears to me not a little extraordinary, that a theory so new, and of such importance, overturning every thing that was thought to be the best established in chemistry, should rest on so very narrow and precarious a foundation, the experiments adduced in support of it being not only ambiguous or explicable on either hypothesis, but exceedingly few. I think I have recited them all, and that on which the greatest stress is laid, viz. That of the formation of water from the decomposition of the two kinds of air, has not been sufficiently repeated. Indeed it required so difficult and expensive an apparatus, and so many precautions in the use of it, that the frequent repetition of the experiment cannot be expected; and in these circumstances the practised experimenter cannot help suspecting the accuracy of the result and consequently the certainty of the conclusion.

One day when the whole family had gone to a circus to see some extraordinary performing apes, I remained alone with my microscope, observing the life in the mobile cells of a transparent star-fish larva, when a new thought suddenly flashed across my brain. It struck me that similar cells might serve in the defence of the organism against intruders. Feeling that there was in this something of surpassing interest, I felt so excited that I began striding up and down the room and even went to the seashore in order to collect my thoughts.I said to myself that, if my supposition was true, a splinter introduced into the body of a star-fish larva, devoid of blood-vessels or of a nervous system, should soon be surrounded by mobile cells as is to be observed in a man who runs a splinter into his finger. This was no sooner said than done.There was a small garden to our dwelling, in which we had a few days previously organised a 'Christmas tree' for the children on a little tangerine tree; I fetched from it a few rose thorns and introduced them at once under the skin of some beautiful star-fish larvae as transparent as water.I was too excited to sleep that night in the expectation of the result of my experiment, and very early the next morning I ascertained that it had fully succeeded.That experiment formed the basis of the phagocyte theory, to the development of which I devoted the next twenty-five years of my life.

Our most successful theories in physics are those that explicitly leave room for the unknown, while confining this room sufficiently to make the theory empirically disprovable. It does not matter whether this room is created by allowing for arbitrary forces as Newtonian dynamics does, or by allowing for arbitrary equations of state for matter, as General Relativity does, or for arbitrary motions of charges and dipoles, as Maxwell's electrodynamics does. To exclude the unknown wholly as a “unified field theory” or a “world equation” purports to do is pointless and of no scientific significance.

Our natural way of thinking about these coarser emotions is that the mental perception of some fact excites the mental affection called the emotion, and that this latter state of mind gives rise to the bodily expression. My theory, on the contrary, is that the bodily changes follow directly the perception of the exciting fact, and that our feeling of the same changes as they occur IS the emotion. Common-sense says, we lose our fortune, are sorry and weep; we meet a bear, are frightened and run; we are insulted by a rival, are angry and strike. The hypothesis here to be defended says that this order of sequence is incorrect, that the one mental state is not immediately induced by the other, that the bodily manifestations must first be interposed between, and that the more rational statement is that we feel sorry because we cry, angry because we strike, afraid because we tremble, and not that we cry, strike, or tremble, because we are sorry, angry, or fearful, as the case may be. Without the bodily states following on the perception, the latter would be purely cognitive in form, pale, colorless, destitute of emotional warmth. We might then see the bear, and judge it best to run, receive the insult and deem it right to strike, but we should not actually feel afraid or angry.

Owing to his lack of knowledge, the ordinary man cannot attempt to resolve conflicting theories of conflicting advice into a single organized structure. He is likely to assume the information available to him is on the order of what we might think of as a few pieces of an enormous jigsaw puzzle. If a given piece fails to fit, it is not because it is fraudulent; more likely the contradictions and inconsistencies within his information are due to his lack of understanding and to the fact that he possesses only a few pieces of the puzzle. Differing statements about the nature of things, differing medical philosophies, different diagnoses and treatments—all of these are to be collected eagerly and be made a part of the individual's collection of puzzle pieces. Ultimately, after many lifetimes, the pieces will fit together and the individual will attain clear and certain knowledge.

Parkinson's Law is a purely scientific discovery, inapplicable except in theory to the politics of the day. It is not the business of the botanist to eradicate the weeds. Enough for him if he can tell us just how fast they grow.

Progress is achieved by exchanging our theories for new ones which go further than the old, until we find one based on a larger number of facts. … Theories are only hypotheses, verified by more or less numerous facts. Those verified by the most facts are the best, but even then they are never final, never to be absolutely believed.

Propose theories which can be criticized. Think about possible decisive falsifying experiments—crucial experiments. But do not give up your theories too easily—not, at any rate, before you have critically examined your criticism.

Psychoanalytic theory is the most stupendous intellectual confidence trick of the twentieth century and a terminal product as well—something akin to a dinosaur or zeppelin in the history of ideas, a vast structure of radically unsound design and with no posterity.

Psychology appeared to be a jungle of confusing, conflicting, and arbitrary concepts. These pre-scientific theories doubtless contained insights which still surpass in refinement those depended upon by psychiatrists or psychologists today. But who knows, among the many brilliant ideas offered, which are the true ones? Some will claim that the statements of one theorist are correct, but others will favour the views of another. Then there is no objective way of sorting out the truth except through scientific research.

Quite recently the human descent theory has been stigmatized as the “gorilla theory of human ancestry.” All this despite the fact that Darwin himself, in the days when not a single bit of evidence regarding the fossil ancestors of man was recognized, distinctly stated that none of the known anthropoid apes, much less any of the known monkeys, should be considered in any way as ancestral to the human stock.

In Henry Fairfield Osborn, 'Osborn States the Case For Evolution', New York Times (12 Jul 1925), XX1. Written at the time of the Scopes Monkey Trial, in rebuttal of the anti-evolution position publicized by William Jennings Bryan.

Reality is what kicks back when you kick it. This is just what physicists do with their particle accelerators. We kick reality and feel it kick back. From the intensity and duration of thousands of those kicks over many years, we have formed a coherent theory of matter and forces, called the standard model, that currently agrees with all observations.

Relativity was a highly technical new theory that gave new meanings to familiar concepts and even to the nature of the theory itself. The general public looked upon relativity as indicative of the seemingly incomprehensible modern era, educated scientists despaired of ever understanding what Einstein had done, and political ideologues used the new theory to exploit public fears and anxieties—all of which opened a rift between science and the broader culture that continues to expand today.

Religious creeds are a great obstacle to any full sympathy between the outlook of the scientist and the outlook which religion is so often supposed to require ... The spirit of seeking which animates us refuses to regard any kind of creed as its goal. It would be a shock to come across a university where it was the practice of the students to recite adherence to Newton's laws of motion, to Maxwell's equations and to the electromagnetic theory of light. We should not deplore it the less if our own pet theory happened to be included, or if the list were brought up to date every few years. We should say that the students cannot possibly realise the intention of scientific training if they are taught to look on these results as things to be recited and subscribed to. Science may fall short of its ideal, and although the peril scarcely takes this extreme form, it is not always easy, particularly in popular science, to maintain our stand against creed and dogma.

Quoted, without citation, in Norman K. Glendenning, Our Place in the Universe (2007), 107. Webmaster has not found any other source for this quote, and cautions doubt about its authenticity. If you know a primary source, please contact Webmaster.

Science deals with judgments on which it is possible to obtain universal agreement. These judgments do not concern individual facts and events, but the invariable association of facts and events known as the laws of science. Agreement is secured by observation and experiment—impartial courts of appeal to which all men must submit if they wish to survive. The laws are grouped and explained by theories of ever increasing generality. The theories at first are ex post facto—merely plausible interpretations of existing bodies of data. However, they frequently lead to predictions that can be tested by experiments and observations in new fields, and, if the interpretations are verified, the theories are accepted as working hypotheses until they prove untenable. The essential requirements are agreement on the subject matter and the verification of predictions. These features insure a body of positive knowledge that can be transmitted from person to person, and that accumulates from generation to generation.

From manuscript on English Science in the Renaissance (1937), Edwin Hubble collection, Box 2, Huntington Library, San Marino, California. As cited by Norriss S. Hetherington in 'Philosophical Values and Observation in Edwin Hubble's Choice of a Model of the Universe', Historical Studies in the Physical Sciences (1982), 13, No. 1, 41. (Hetherington comments parenthetically that the references to court, judgment and appeal may be attributable to his prior experiences as a Rhodes Scholar reading Roman law at Oxford, and to a year's practice as an attorney in Louisville, Kentucky.)

Science does not rest upon solid bedrock. The bold structure of its theories rises, as it were, above a swamp. It is like a building erected on piles. The piles are driven down from above into the swamp, but not down to any natural or 'given' base; and when we cease our attempts to drive our piles into a deeper layer, it is not because we have reached firm ground. We simply stop when we are satisfied that they are firm enough to carry the structure, at least for the time being. (1959)

Science has hitherto been proceeding without the guidance of any rational theory of logic, and has certainly made good progress. It is like a computer who is pursuing some method of arithmetical approximation. Even if he occasionally makes mistakes in his ciphering, yet if the process is a good one they will rectify themselves. But then he would approximate much more rapidly if he did not commit these errors; and in my opinion, the time has come when science ought to be provided with a logic. My theory satisfies me; I can see no flaw in it. According to that theory universality, necessity, exactitude, in the absolute sense of these words, are unattainable by us, and do not exist in nature. There is an ideal law to which nature approximates; but to express it would require an endless series of modifications, like the decimals expressing surd. Only when you have asked a question in so crude a shape that continuity is not involved, is a perfectly true answer attainable.

Seven American Nights (1978). In the collection, David G. Hartwell (Ed.), The Dark Descent (1997), 653.

Science in England, in America, is jealous of theory, hates the name of love and moral purpose. There's revenge for this humanity. What manner of man does science make? The boy is not attracted. He says, I do not wish to be such a kind of man as my professor is.

Science is in a literal sense constructive of new facts. It has no fixed body of facts passively awaiting explanation, for successful theories allow the construction of new instruments—electron microscopes and deep space probes—and the exploration of phenomena that were beyond description—the behavior of transistors, recombinant DNA, and elementary particles, for example. This is a key point in the progressive nature of science—not only are there more elegant or accurate analyses of phenomena already known, but there is also extension of the range of phenomena that exist to be described and explained.Co-author with Michael A. Arbib, English-born professor of computer science and biomedical engineering (1940-)

Science is uncertain. Theories are subject to revision; observations are open to a variety of interpretations, and scientists quarrel amongst themselves. This is disillusioning for those untrained in the scientific method, who thus turn to the rigid certainty of the Bible instead. There is something comfortable about a view that allows for no deviation and that spares you the painful necessity of having to think.

Scientific discovery, or the formulation of scientific theory, starts in with the unvarnished and unembroidered evidence of the senses. It starts with simple observation—simple, unbiased, unprejudiced, naive, or innocent observation—and out of this sensory evidence, embodied in the form of simple propositions or declarations of fact, generalizations will grow up and take shape, almost as if some process of crystallization or condensation were taking place. Out of a disorderly array of facts, an orderly theory, an orderly general statement, will somehow emerge.

Scientific theories need reconstruction every now and then. If they didn't need reconstruction they would be facts, not theories. The more facts we know, the less radical become the changes in our theories. Hence they are becoming more and more constant. But take the theory of gravitation; it has not been changed in four hundred years.

Scientists can only carry on with their work, addressing legitimate questions as they arise and challenging misinformation. … Scientists work to fill the gaps in human knowledge and to build a theory that can explain observations of the world. Climate sceptics revel in such gaps, sometimes long after they have been filled.

The Bee (c.1902). In What is Man? And Other Essays (1917), 283. Reprinted in Charles Neider (ed.), Complete Essays (1963). In Mark Twain and Brian Collins (ed.), When in Doubt, Tell the Truth: and Other Quotations from Mark Twain (1996), 118.

Scientists, therefore, are responsible for their research, not only intellectually but also morally. This responsibility has become an important issue in many of today's sciences, but especially so in physics, in which the results of quantum mechanics and relativity theory have opened up two very different paths for physicists to pursue. They may lead us—to put it in extreme terms—to the Buddha or to the Bomb, and it is up to each of us to decide which path to take.

Since religion intrinsically rejects empirical methods, there should never be any attempt to reconcile scientific theories with religion. [An infinitely old universe, always evolving may not be compatible with the Book of Genesis. However, religions such as Buddhism get along without having any explicit creation mythology and are in no way contradicted by a universe without a beginning or end.] Creatio ex nihilo, even as religious doctrine, only dates to around AD 200. The key is not to confuse myth and empirical results, or religion and science.

Since the beginning of physics, symmetry considerations have provided us with an extremely powerful and useful tool in our effort to understand nature. Gradually they have become the backbone of our theoretical formulation of physical laws.

Students using astrophysical textbooks remain essentially ignorant of even the existence of plasma concepts, despite the fact that some of them have been known for half a century. The conclusion is that astrophysics is too important to be left in the hands of astrophysicists who have gotten their main knowledge from these textbooks. Earthbound and space telescope data must be treated by scientists who are familiar with laboratory and magnetospheric physics and circuit theory, and of course with modern plasma theory.[Lamenting the traditional neglect of plasma physics]

Such an atmosphere is un-American, the most un-American thing we have to contend with today. It is the climate of a totalitarian country in which scientists are expected to change their theories to match changes in the police state's propaganda line.[Stinging rebuke of J. Parnell Thomas, Chairman, House Committee on Un-American activities, who had attacked Dr. Condon (1 Mar 1948) as a weak link in American atomic security.]

Opening address (13 Sep 1953) at the annual meeting of the American Association for the Advancement of Science where Condon would be elected as the new AAAS president. Obituary, New York Times (27 Mar 1974), 46.

Suppose a number of equal waves of water to move upon the surface of a stagnant lake, with a certain constant velocity, and to enter a narrow channel leading out of the lake. Suppose then another similar cause to have excited another equal series of waves, which arrive at the same time, with the first. Neither series of waves will destroy the other, but their effects will be combined: if they enter the channel in such a manner that the elevations of one series coincide with those of the other, they must together produce a series of greater joint elevations; but if the elevations of one series are so situated as to correspond to the depressions of the other, they must exactly fill up those depressions. And the surface of the water must remain smooth; at least I can discover no alternative, either from theory or from experiment.

Take the rose—most people think it very beautiful: I don’t care for It at all. I prefer the cactus, for the simple reason that it has a more interesting personality. It has wonderfully adapted itself to its surroundings! It is the best illustration of the theory of evolution in plant life.

That is the way of the scientist. He will spend thirty years in building up a mountain range of facts with the intent to prove a certain theory; then he is so happy with his achievement that as a rule he overlooks the main chief fact of all—that all his accumulation proves an entirely different thing.

That our knowledge only illuminates a small corner of the Universe, that it is incomplete, approximate, tentative and merely probable need not concert us. It is genuine nevertheless. Physical science stands as one of the great achievements of the human spirit.

That the Anatomy of the Nerves yields more pleasant and profitable Speculations, than the Theory of any parts besides in the animated Body: for from hence the true and genuine Reasons are drawn of very many Actions and Passions that are wont to happen in our Body, which otherwise seem most difficult and unexplicable; and no less from this Fountain the hidden Causes of Diseases and their Symptoms, which commonly are ascribed to the Incantations of Witches, may be found out and clearly laid open. But as to our observations about the Nerves, from our following Discourse it will plainly appear, that I have not trod the paths or footsteps of others, nor repeated what hath been before told.

The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognisable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past. One must not think then that the old-fashioned theories have been sterile and vain.

The aether: Invented by Isaac Newton, reinvented by James Clerk Maxwell. This is the stuff that fills up the empty space of the universe. Discredited and discarded by Einstein, the aether is now making a Nixonian comeback. It’s really the vacuum, but burdened by theoretical, ghostly particles.

The ancestors of the higher animals must be regarded as one-celled beings, similar to the Amœbæ which at the present day occur in our rivers, pools, and lakes. The incontrovertible fact that each human individual develops from an egg, which, in common with those of all animals, is a simple cell, most clearly proves that the most remote ancestors of man were primordial animals of this sort, of a form equivalent to a simple cell. When, therefore, the theory of the animal descent of man is condemned as a “horrible, shocking, and immoral” doctrine, tho unalterable fact, which can be proved at any moment under the microscope, that the human egg is a simple cell, which is in no way different to those of other mammals, must equally be pronounced “horrible, shocking, and immoral.”

The basic thesis of gestalt theory might be formulated thus: there are contexts in which what is happening in the whole cannot be deduced from the characteristics of the separate pieces, but conversely; what happens to a part of the whole is, in clearcut cases, determined by the laws of the inner structure of its whole.

The best class of scientific mind is the same as the best class of business mind. The great desideratum in either case is to know how much evidence is enough to warrant action. It is as unbusiness-like to want too much evidence before buying or selling as to be content with too little. The same kind of qualities are wanted in either case. The difference is that if the business man makes a mistake, he commonly has to suffer for it, whereas it is rarely that scientific blundering, so long as it is confined to theory, entails loss on the blunderer. On the contrary it very often brings him fame, money and a pension. Hence the business man, if he is a good one, will take greater care not to overdo or underdo things than the scientific man can reasonably be expected to take.

The Big Idea that had been developed in the seventeenth century ... is now known as the scientific method. It says that the way to proceed when investigating how the world works is to first carry out experiments and/or make observations of the natural world. Then, develop hypotheses to explain these observations, and (crucially) use the hypothesis to make predictions about the future outcome of future experiments and/or observations. After comparing the results of those new observations with the predictions of the hypotheses, discard those hypotheses which make false predictions, and retain (at least, for the time being) any hypothesis that makes accurate predictions, elevating it to the status of a theory. Note that a theory can never be proved right. The best that can be said is that it has passed all the tests applied so far.

The chemist in America has in general been content with what I have called a loafer electron theory. He has imagined the electrons sitting around on dry goods boxes at every corner [viz. the cubic atom], ready to shake hands with, or hold on to similar loafer electrons in other atoms.

The complacent manner in which geologists have produced their theories has been extremely amusing; for often with knowledge (and that frequently inaccurate) not extending beyond a given province, they have described the formation of a world with all the detail and air of eye-witnesses. That much good ensues, and that the science is greatly advanced, by the collision of various theories, cannot be doubted. Each party is anxious to support opinions by facts. Thus, new countries are explored, and old districts re-examined; facts come to light that do not suit either party; new theories spring up; and, in the end, a greater insight into the real structure of the earth's surface is obtained.

'The Origin of Hypotheses, illustrated by the Discussion of a Topographical Problem', Science, 1896, 3, 2.

The contents of this section will furnish a very striking illustration of the truth of a remark, which I have more than once made in my philosophical writings, and which can hardly be too often repeated, as it tends greatly to encourage philosophical investigations viz. That more is owing to what we call chance, that is, philosophically speaking, to the observation of events arising from unknown causes, than to any proper design, or pre-conceived theory in this business. This does not appear in the works of those who write synthetically upon these subjects; but would, I doubt not, appear very strikingly in those who are the most celebrated for their philosophical acumen, did they write analytically and ingenuously.

The description of some of the experiments, which are communicated here, was completely worked out at my writing-table, before I had seen anything of the phenomena in question. After making the experiments on the following day, it was found that nothing in the description required to be altered. I do not mention this from feelings of pride, but in order to make clear the extraordinary ease and security with which the relations in question can be considered on the principles of Arrhenius' theory of free ions. Such facts speak more forcibly then any polemics for the value of this theory .

The development of mathematics is largely a natural, not a purely logical one: mathematicians are continually answering questions suggested by astronomers or physicists; many essential mathematical theories are but the reflex outgrowth from physical puzzles.

The difference between myth and science is the difference between divine inspiration of 'unaided reason' (as Bertrand Russell put it) on the one hand and theories developed in observational contact with the real world on the other. It is the difference between the belief in prophets and critical thinking, between Credo quia absurdum (I believe because it is absurd–Tertullian) and De omnibus est dubitandum (Everything should be questioned–Descartes). To try to write a grand cosmical drama leads necessarily to myth. To try to let knowledge substitute ignorance in increasingly large regions of space and time is science.

The difficulties connected with my criterion of demarcation (D) are important, but must not be exaggerated. It is vague, since it is a methodological rule, and since the demarcation between science and nonscience is vague. But it is more than sharp enough to make a distinction between many physical theories on the one hand, and metaphysical theories, such as psychoanalysis, or Marxism (in its present form), on the other. This is, of course, one of my main theses; and nobody who has not understood it can be said to have understood my theory.The situation with Marxism is, incidentally, very different from that with psychoanalysis. Marxism was once a scientific theory: it predicted that capitalism would lead to increasing misery and, through a more or less mild revolution, to socialism; it predicted that this would happen first in the technically highest developed countries; and it predicted that the technical evolution of the 'means of production' would lead to social, political, and ideological developments, rather than the other way round.But the (so-called) socialist revolution came first in one of the technically backward countries. And instead of the means of production producing a new ideology, it was Lenin's and Stalin's ideology that Russia must push forward with its industrialization ('Socialism is dictatorship of the proletariat plus electrification') which promoted the new development of the means of production.Thus one might say that Marxism was once a science, but one which was refuted by some of the facts which happened to clash with its predictions (I have here mentioned just a few of these facts).However, Marxism is no longer a science; for it broke the methodological rule that we must accept falsification, and it immunized itself against the most blatant refutations of its predictions. Ever since then, it can be described only as nonscience—as a metaphysical dream, if you like, married to a cruel reality.Psychoanalysis is a very different case. It is an interesting psychological metaphysics (and no doubt there is some truth in it, as there is so often in metaphysical ideas), but it never was a science. There may be lots of people who are Freudian or Adlerian cases: Freud himself was clearly a Freudian case, and Adler an Adlerian case. But what prevents their theories from being scientific in the sense here described is, very simply, that they do not exclude any physically possible human behaviour. Whatever anybody may do is, in principle, explicable in Freudian or Adlerian terms. (Adler's break with Freud was more Adlerian than Freudian, but Freud never looked on it as a refutation of his theory.)The point is very clear. Neither Freud nor Adler excludes any particular person's acting in any particular way, whatever the outward circumstances. Whether a man sacrificed his life to rescue a drowning, child (a case of sublimation) or whether he murdered the child by drowning him (a case of repression) could not possibly be predicted or excluded by Freud's theory; the theory was compatible with everything that could happen—even without any special immunization treatment.Thus while Marxism became non-scientific by its adoption of an immunizing strategy, psychoanalysis was immune to start with, and remained so. In contrast, most physical theories are pretty free of immunizing tactics and highly falsifiable to start with. As a rule, they exclude an infinity of conceivable possibilities.

The dimmed outlines of phenomenal things all merge into one another unless we put on the focusing-glass of theory, and screw it up sometimes to one pitch of definition and sometimes to another, so as to see down into different depths through the great millstone of the world.

Are There Real Analogies in Nature?' (Feb 1856). Quoted in Lewis Campbell and William GarnettThe Life of James Clerk Maxwell (1882), 237.

The discovery of the telephone has made us acquainted with many strange phenomena. It has enabled us, amongst other things, to establish beyond a doubt the fact that electric currents actually traverse the earth's crust. The theory that the earth acts as a great reservoir for electricity may be placed in the physicist's waste-paper basket, with phlogiston, the materiality of light, and other old-time hypotheses.

The discovery which has been pointed to by theory is always one of profound interest and importance, but it is usually the close and crown of a long and fruitful period, whereas the discovery which comes as a puzzle and surprise usually marks a fresh epoch and opens a new chapter in science.

The engineer is concerned to travel from the abstract to the concrete. He begins with an idea and ends with an object. He journeys from theory to practice. The scientist’s job is the precise opposite. He explores nature with his telescopes or microscopes, or much more sophisticated techniques, and feeds into a computer what he finds or sees in an attempt to define mathematically its significance and relationships. He travels from the real to the symbolic, from the concrete to the abstract. The scientist and the engineer are the mirror image of each other.

The entire annals of Observation probably do not elsewhere exhibit so extraordinary a verification of any theoretical conjecture adventured on by the human spirit![On the mathematical work by Urbain Le Verrier predicting the planet Neptune.]

In The Planet Neptune: An Exposition and History (1848), 90. The verification of the existence of the planet Neptune was made when Johan Galle found a star in an evening observation at the position predicted in the letter he received from Le Verrier earlier that same day.

The evolution of higher and of lower forms of life is as well and as soundly established as the eternal hills. It has long since ceased to be a theory; it is a law of Nature as universal in living things as is the law of gravitation in material things and in the motions of the heavenly spheres.

The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.

The experimental investigation by which Ampere established the law of the mechanical action between electric currents is one of the most brilliant achievements in science. The whole theory and experiment, seems as if it had leaped, full grown and full armed, from the brain of the 'Newton of Electricity'. It is perfect in form, and unassailable in accuracy, and it is summed up in a formula from which all the phenomena may be deduced, and which must always remain the cardinal formula of electro-dynamics.

The extracellular genesis of cells in animals seemed to me, ever since the publication of the cell theory [of Schwann], just as unlikely as the spontaneous generation of organisms. These doubts produced my observations on the multiplication of blood cells by division in bird and mammalian embryos and on the division of muscle bundles in frog larvae. Since then I have continued these observations in frog larvae, where it is possible to follow the history of tissues back to segmentation.

The fact that Science walks forward on two feet, namely theory and experiment, is nowhere better illustrated than in the two fields for slight contributions to which you have done me the great honour of awarding the the Nobel Prize in Physics for the year 1923. Sometimes it is one foot that is put forward first, sometimes the other, but continuous progress is only made by the use of both—by theorizing and then testing, or by finding new relations in the process of experimenting and then bringing the theoretical foot up and pushing it on beyond, and so on in unending alterations.

The farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separated branches of the science.

In 'Mathematical Problems', Lecture at the International Congress of Mathematics, Paris, (8 Aug 1900). Translated by Dr. Maby Winton Newson in Bulletin of the American Mathematical Society (1902), 8, 479.

The fundamental biological variant is DNA. That is why Mendel's definition of the gene as the unvarying bearer of hereditary traits, its chemical identification by Avery (confirmed by Hershey), and the elucidation by Watson and Crick of the structural basis of its replicative invariance, are without any doubt the most important discoveries ever made in biology. To this must be added the theory of natural selection, whose certainty and full significance were established only by those later theories.

The generalized theory of relativity has furnished still more remarkable results. This considers not only uniform but also accelerated motion. In particular, it is based on the impossibility of distinguishing an acceleration from the gravitation or other force which produces it. Three consequences of the theory may be mentioned of which two have been confirmed while the third is still on trial: (1) It gives a correct explanation of the residual motion of forty-three seconds of arc per century of the perihelion of Mercury. (2) It predicts the deviation which a ray of light from a star should experience on passing near a large gravitating body, the sun, namely, 1".7. On Newton's corpuscular theory this should be only half as great. As a result of the measurements of the photographs of the eclipse of 1921 the number found was much nearer to the prediction of Einstein, and was inversely proportional to the distance from the center of the sun, in further confirmation of the theory. (3) The theory predicts a displacement of the solar spectral lines, and it seems that this prediction is also verified.

The history of acceptance of new theories frequently shows the following steps: At first the new idea is treated as pure nonsense, not worth looking at. Then comes a time when a multitude of contradictory objections are raised, such as: the new theory is too fancy, or merely a new terminology; it is not fruitful, or simply wrong. Finally a state is reached when everyone seems to claim that he had always followed this theory. This usually marks the last state before general acceptance.

The history of science shows so many examples of the 'irrational' notions and theories of to-day becoming the 'rational' notions and theories of to-morrow, that it seems largely a matter of being accustomed to them whether they are considered rational or not, natural or not.

The incomplete knowledge of a system must be an essential part of every formulation in quantum theory. Quantum theoretical laws must be of a statistical kind. To give an example: we know that the radium atom emits alpha-radiation. Quantum theory can give us an indication of the probability that the alpha-particle will leave the nucleus in unit time, but it cannot predict at what precise point in time the emission will occur, for this is uncertain in principle.

The intensity and quantity of polemical literature on scientific problems frequently varies inversely as the number of direct observations on which the discussions are based: the number and variety of theories concerning a subject thus often form a coefficient of our ignorance. Beyond the superficial observations, direct and indirect, made by geologists, not extending below about one two-hundredth of the Earth's radius, we have to trust to the deductions of mathematicians for our ideas regarding the interior of the Earth; and they have provided us successively with every permutation and combination possible of the three physical states of matter—solid, liquid, and gaseous.

'Address delivered by the President of Section [Geology] at Sydney (Friday, Aug 21), Report of the Eighty-Fourth Meeting of the British Association for the Advancement of Science: Australia 1914, 1915, 345.

The laws of science are the permanent contributions to knowledge—the individual pieces that are fitted together in an attempt to form a picture of the physical universe in action. As the pieces
fall into place, we often catch glimpses of emerging patterns, called theories; they set us searching for the missing pieces that will fill in the gaps and complete the patterns. These theories, these provisional interpretations of the data in hand, are mere working hypotheses, and they are treated with scant respect until they can be tested by new pieces of the puzzle.

The layman, taught to revere scientists for their absolute respect for the observed facts, and for the judiciously detached and purely provisional manner in which they hold scientific theories (always ready to abandon a theory at the sight of any contradictory evidence) might well have thought that, at [Dayton C.] Miller's announcement of this overwhelming evidence of a “positive effect” [indicating that the speed of light is not independent from the motion of the observer, as Einstein's theory of relativity demands] in his presidential address to the American Physical Society on December 29th, 1925, his audience would have instantly abandoned the theory of relativity. Or, at the very least, that scientists—wont to look down from the pinnacle of their intellectual humility upon the rest of dogmatic mankind—might suspend judgment in this matter until Miller's results could be accounted for without impairing the theory of relativity. But no: by that time they had so well closed their minds to any suggestion which threatened the new rationality achieved by Einstein's world-picture, that it was almost impossible for them to think again in different terms. Little attention was paid to the experiments, the evidence being set aside in the hope that it would one day turn out to be wrong.

Personal Knowledge: Towards a Post-Critical Philosophy (1958, 1998), 13. Miller had earlier presented his evidence against the validity of the relativity theory at the annual meeting, 28 Apr 1925, of the National Academy of Sciences. Miller believed he had, by a much-refined and improved repetition of the so-called Michelson-Morley experiment, shown that there is a definite and measurable motion of the earth through the ether. In 1955, a paper by R.S. Shankland, et al., in Rev. Modern Phys. (1955), 27, 167, concluded that statistical fluctuations and temperature effects in the data had simulated what Miller had taken to be he apparent ether drift.

The lessons of science should be experimental also. The sight of a planet through a telescope is worth all the course on astronomy; the shock of the electric spark in the elbow outvalues all theories; the taste of the nitrous oxide, the firing of an artificial volcano, are better than volumes of chemistry.

The longing to behold this pre-established harmony [of phenomena and theoretical principles] is the source of the inexhaustible patience and perseverance with which Planck has devoted himself ... The state of mind which enables a man to do work of this kind is akin to that of the religious worshiper or the lover; the daily effort comes from no deliberate intention or program, but straight from the heart.

The mathematicians have been very much absorbed with finding the general solution of algebraic equations, and several of them have tried to prove the impossibility of it. However, if I am not mistaken, they have not as yet succeeded. I therefore dare hope that the mathematicians will receive this memoir with good will, for its purpose is to fill this gap in the theory of algebraic equations.

Opening of Memoir on Algebraic Equations, Proving the Impossibility of a Solution of the General Equation of the Fifth Degree. The paper was originally published (1824) in French, as a pamphlet, in Oslo. Collected in Œuvres Complètes (1881), Vol. 1, 28. Translation by W.H. Langdon collected in David Eugene Smith, A Source Book in Mathematics (2012), 261. In this work, he showed why—despite two centuries of efforts by mathematicians—solving equations of the fifth degree would remain futile. The insights from this paper led to the modern theory of equations.

The method of inquiry which all our ingenious Theorists of the Earth have pursued is certainly erroneous. They first form an hypothesis to solve the phenomena, but in fact the Phenomena are always used as a prop to the hypothesis.Instead therefore of attempting to cut the gordian knot by Hypothetical analysis, we shall follow the synthetic method of inquiry and content ourselves with endeavouring to establish facts rather than attempt solutions and try by experiments how far that method may leave us thro' the mazes of this subject

The method of science depends on our attempts to describe the world with simple theories: theories that are complex may become untestable, even if they happen to be true. Science may be described as the art of systematic over-simplification—the art of discerning what we may with advantage omit.

The moment one has offered an original explanation for a phenomenon which seems satisfactory, that moment affection for his intellectual child springs into existence, and as the explanation grows into a definite theory his parental affections cluster about his offspring and it grows more and more dear to him. ... There springs up also unwittingly a pressing of the theory to make it fit the facts and a pressing of the facts to make them fit the theory... To avoid this grave danger, the method of multiple working hypotheses is urged. It differs from the simple working hypothesis in that it distributes the effort and divides the affections... In developing the multiple hypotheses, the effort is to bring up into view every rational exploration of the phenomenon in hand and to develop every tenable hypothesis relative to its nature, cause or origin, and to give to all of these as impartially as possible a working form and a due place in the investigation. The investigator thus becomes the parent of a family of hypotheses; and by his parental relations to all is morally forbidden to fasten his affections unduly upon anyone. ... Each hypothesis suggests its own criteria, its own method of proof, its own method of developing the truth, and if a group of hypotheses encompass the subject on all sides, the total outcome of means and of methods is full and rich.

The more experiences and experiments accumulate in the exploration of nature, the more precarious the theories become. But it is not always good to discard them immediately on this account. For every hypothesis which once was sound was useful for thinking of previous phenomena in the proper interrelations and for keeping them in context. We ought to set down contradictory experiences separately, until enough have accumulated to make building a new structure worthwhile.

The Newton of drift theory has not yet appeared. His absence need cause no anxiety; the theory is still young and still often treated with suspicion. In the long run, one cannot blame a theoretician for hesitating to spend time and trouble on explaining a law about whose validity no unanimity prevails.

The old scientific ideal of episteme — of absolutely certain, demonstrable knowledge — has proved to be an idol. The demand for scientific objectivity makes it inevitable that every scientific statement must remain tentative for ever. (1959)

The only sure foundations of medicine are, an intimate knowledge of the human body, and observation on the effects of medicinal substances on that. The anatomical and clinical schools, therefore, are those in which the young physician should be formed. If he enters with innocence that of the theory of medicine, it is scarcely possible he should come out untainted with error. His mind must be strong indeed, if, rising above juvenile credulity, it can maintain a wise infidelity against the authority of his instructors, and the bewitching delusions of their theories.

The philosopher of science is not much interested in the thought processes which lead to scientific discoveries; he looks for a logical analysis of the completed theory, including the establishing its validity. That is, he is not interested in the context of discovery, but in the context of justification.

The physiological combustion theory takes as its starting point the fundamental principle that the amount of heat that arises from the combustion of a given substance is an invariable quantity–i.e., one independent of the circumstances accompanying the combustion–from which it is more specifically concluded that the chemical effect of the combustible materials undergoes no quantitative change even as a result of the vital process, or that the living organism, with all its mysteries and marvels, is not capable of generating heat out of nothing.

The present state of the system of nature is evidently a consequence of what it was in the preceding moment, and if we conceive of an intelligence that at a given instant comprehends all the relations of the entities of this universe, it could state the respective position, motions, and general affects of all these entities at any time in the past or future. Physical astronomy, the branch of knowledge that does the greatest honor to the human mind, gives us an idea, albeit imperfect, of what such an intelligence would be. The simplicity of the law by which the celestial bodies move, and the relations of their masses and distances, permit analysis to follow their motions up to a certain point; and in order to determine the state of the system of these great bodies in past or future centuries, it suffices for the mathematician that their position and their velocity be given by observation for any moment in time. Man owes that advantage to the power of the instrument he employs, and to the small number of relations that it embraces in its calculations. But ignorance of the different causes involved in the production of events, as well as their complexity, taken together with the imperfection of analysis, prevents our reaching the same certainty about the vast majority of phenomena. Thus there are things that are uncertain for us, things more or less probable, and we seek to compensate for the impossibility of knowing them by determining their different degrees of likelihood. So it was that we owe to the weakness of the human mind one of the most delicate and ingenious of mathematical theories, the science of chance or probability.

The quantum entered physics with a jolt. It didn’t fit anywhere; it made no sense; it contradicted everything we thought we knew about nature. Yet the data seemed to demand it. ... The story of Werner Heisenberg and his science is the story of the desperate failures and ultimate triumphs of the small band of brilliant physicists who—during an incredibly intense period of struggle with the data, the theories, and each other during the 1920s—brought about a revolutionary new understanding of the atomic world known as quantum mechanics.

The recurrence of a phenomenon like Edison is not very likely. The profound change of conditions and the ever increasing necessity of theoretical training would seem to make it impossible. He will occupy a unique and exalted position in the history of his native land, which might well be proud of his great genius and undying achievements in the interest of humanity.

The scientist explores the world of phenomena by successive approximations. He knows that his data are not precise and that his theories must always be tested. It is quite natural that he tends to develop healthy skepticism, suspended judgment, and disciplined imagination.

The scientist knows that the ultimate of everything is unknowable. No matter What subject you take, the current theory of it if carried to the ultimate becomes ridiculous. Time and space are excellent examples of this.

The starting point of Darwin’s theory of evolution is precisely the existence of those differences between individual members of a race or species which morphologists for the most part rightly neglect. The first condition necessary, in order that any process of Natural Selection may begin among a race, or species, is the existence of differences among its members; and the first step in an enquiry into the possible effect of a selective process upon any character of a race must be an estimate of the frequency with which individuals, exhibiting any given degree of abnormality with respect to that, character, occur. The unit, with which such an enquiry must deal, is not an individual but a race, or a statistically representative sample of a race; and the result must take the form of a numerical statement, showing the relative frequency with which the various kinds of individuals composing the race occur.

The struggle for existence holds as much in the intellectual as in the physical world. A theory is a species of thinking, and its right to exist is coextensive with its power of resisting extinction by its rivals.

The study of mathematics is apt to commence in disappointment. The important applications of the science, the theoretical interest of its ideas, and the logical rigour of its methods all generate the expectation of a speedy introduction to processes of interest. We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it.

The success of the paradigm... is at the start largely a promise of success ... Normal science consists in the actualization of that promise... Mopping up operations are what engage most scientists throughout their careers. They constitute what I am here calling normal science... That enterprise seems an attempt to force nature into the preformed and relatively inflexible box that the paradigm supplies. No part of the aim of normal science is to call forth new sorts of phenomena; indeed those that will not fit the box are often not seen at all. Nor do scientists normally aim to invent new theories, and they are often intolerant of those invented by others.

The test of a theory is its ability to cope with all the relevant phenomena, not its a priori 'reasonableness'. The latter would have proved a poor guide in the development of science, which often makes progress by its encounter with the totally unexpected and initially extremely puzzling.

The theoretical broadening which comes from having many humanities subjects on the campus is offset by the general dopiness of the people who study these things and by the Department of Home Economics.

The theoretical idea … does not arise apart from and independent of experience; nor can it be derived from experience by a purely logical procedure. It is produced by a creative act. Once a theoretical idea has been acquired, one does well to hold fast to it until it leads to an untenable conclusion.

The theoretical side of physical chemistry is and will probably remain the dominant one; it is by this peculiarity that it has exerted such a great influence upon the neighboring sciences, pure and applied, and on this ground physical chemistry may be regarded as an excellent school of exact reasoning for all students of the natural sciences.

The theory here developed is that mega-evolution normally occurs among small populations that become preadaptive and evolve continuously (without saltation, but at exceptionally rapid rates) to radically different ecological positions. The typical pattern involved is probably this: A large population is fragmented into numerous small isolated lines of descent. Within these, inadaptive differentiation and random fixation of mutations occur. Among many such inadaptive lines one or a few are preadaptive, i.e., some of their characters tend to fit them for available ecological stations quite different from those occupied by their immediate ancestors. Such groups are subjected to strong selection pressure and evolve rapidly in the further direction of adaptation to the new status. The very few lines that successfully achieve this perfected adaptation then become abundant and expand widely, at the same time becoming differentiated and specialized on lower levels within the broad new ecological zone.

The theory of probabilities is at bottom only common sense reduced to calculation; it makes us appreciate with exactitude what reasonable minds feel by a sort of instinct, often without being able to account for it. … It is remarkable that [this] science, which originated in the consideration of games of chance, should have become the most important object of human knowledge.

The theory of probabilities is basically only common sense reduced to a calculus. It makes one estimate accurately what right-minded people feel by a sort of instinct, often without being able to give a reason for it.

The Theory of Relativity confers an absolute meaning on a magnitude which in classical theory has only a relative significance: the velocity of light. The velocity of light is to the Theory of Relativity as the elementary quantum of action is to the Quantum Theory: it is its absolute core.

The theory of the earth is the science which describes and explains changes that the terrestrial globe has undergone from its beginning until today, and which allows the prediction of those it shall undergo in the future. The only way to understand these changes and their causes is to study the present-day state of the globe in order to gradually reconstruct its earlier stages, and to develop probable hypotheses on its future state. Therefore, the present state of the earth is the only solid base on which the theory can rely.

The theory of the lung as a gland has justified its existence and done excellent service in bringing forward facts, which shall survive any theoretical construction that has been or may hereafter be put upon them.

The theory that gravitational attraction is inversely proportional to the square of the distance leads by remorseless logic to the conclusion that the path of a planet should be an ellipse .... It is this logical thinking that is the real meat of the physical sciences. The social scientist keeps the skin and throws away the meat.... His theorems no more follow from his postulates than the hunches of a horse player follow logically from the latest racing news. The result is guesswork clad in long flowing robes of gobbledygook.

The transition from a paradigm in crisis to a new one from which a new tradition of normal science can emerge is far from a cumulative process, one achieved by an articulation or extension of the old paradigm. Rather it is a reconstruction of the field from new fundamentals, a reconstruction that changes some of the field's most elementary theoretical generalizations as well as many of its paradigm methods and applications. During the transition period there will be a large but never complete overlap between the problems that can be solved by the old and by the new paradigm. But there will also be a decisive difference in the modes of solution. When the transition is complete, the profession will have changed its view of the field, its methods, and its goals.

The universe came into being in a big bang, before which, Einstein’s theory instructs us, there was no before. Not only particles and fields of force had to come into being at the big bang, but the laws of physics themselves, and this by a process as higgledy-piggledy as genetic mutation or the second law of thermodynamics.

The universe is governed by science. But science tells us that we can’t solve the equations, directly in the abstract. We need to use the effective theory of Darwinian natural selection of those societies most likely to survive. We assign them higher value.[Answer to question: What is the value in knowing “Why are we here?”]

The velocity of light is one of the most important of the fundamental constants of Nature. Its measurement by Foucault and Fizeau gave as the result a speed greater in air than in water, thus deciding in favor of the undulatory and against the corpuscular theory. Again, the comparison of the electrostatic and the electromagnetic units gives as an experimental result a value remarkably close to the velocity of light–a result which justified Maxwell in concluding that light is the propagation of an electromagnetic disturbance. Finally, the principle of relativity gives the velocity of light a still greater importance, since one of its fundamental postulates is the constancy of this velocity under all possible conditions.

The world little knows how many of the thoughts and theories which have passed through the mind of a scientific investigator, have been crushed in silence and secrecy by his own severe criticism and adverse examination!

The young specialist in English Lit, having quoted me, went on to lecture me severely on the fact that in every century people have thought they understood the Universe at last, and in every century they were proved to be wrong. It follows that the one thing we can say about our modern “knowledge” is that it is wrong.The young man then quoted with approval what Socrates had said on learning that the Delphic oracle had proclaimed him the wisest man in Greece. “If I am the wisest man,” said Socrates, “it is because I alone know that I know nothing.” The implication was that I was very foolish because I was under the impression I knew a great deal.Alas, none of this was new to me. (There is very little that is new to me; I wish my correspondents would realize this.) This particular theme was addressed to me a quarter of a century ago by John Campbell, who specialized in irritating me. He also told me that all theories are proven wrong in time.My answer to him was, “John, when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical, they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together.”

Their theories should be carefully examined and their arguments fairly weighed, but the scientist cannot compel acceptance of any argument he advances, except as, judged upon its merits, it is convincing.

Theories cannot claim to be indestructible. They are only the plough which the ploughman uses to draw his furrow and which he has every right to discard for another one, of improved design, after the harvest. To be this ploughman, to see my labours result in the furtherance of scientific progress, was the height of my ambition, and now the Swedish Academy of Sciences has come, at this harvest, to add the most brilliant of crowns.

Theory and fact are equally strong and utterly interdependent; one has no meaning without the other. We need theory to organize and interpret facts, even to know what we can or might observe. And we need facts to validate theories and give them substance.

There are 60 sub-atomic particles they’ve discovered that can explain the thousands of other sub-atomic particles, and the model is too ugly. This is my analogy: it’s like taking Scotch tape and taping a giraffe to a mule to a whale to a tiger and saying this is the ultimate theory of particles. … We have so many particles that Oppenheimer once said you could give a Nobel Prize to the physicist that did not discover a particle that year. We were drowning in sub-atomic particles.Now we realize that this whole zoo of sub-atomic particles, thousands of them coming out of our accelerators, can be explained by little vibrating strings.

There are many examples of old, incorrect theories that stubbornly persisted, sustained only by the prestige of foolish but well-connected scientists. ... Many of these theories have been killed off only when some decisive experiment exposed their incorrectness.

There are some modern practitioners, who declaim against medical theory in general, not considering that to think is to theorize; and that no one can direct a method of cure to a person labouring under disease, without thinking, that is, without theorizing; and happy therefore is the patient, whose physician possesses the best theory.

There are still psychologists who, in a basic misunderstanding, think that gestalt theory tends to underestimate the role of past experience. Gestalt theory tries to differentiate between and-summative aggregates, on the one hand, and gestalten, structures, on the other, both in sub-wholes and in the total field, and to develop appropriate scientific tools for investigating the latter. It opposes the dogmatic application to all cases of what is adequate only for piecemeal aggregates. The question is whether an approach in piecemeal terms, through blind connections, is or is not adequate to interpret actual thought processes and the role of the past experience as well. Past experience has to be considered thoroughly, but it is ambiguous in itself; so long as it is taken in piecemeal, blind terms it is not the magic key to solve all problems.

There is a great deal of emotional satisfaction in the elegant demonstration, in the elegant ordering of facts into theories, and in the still more satisfactory, still more emotionally exciting discovery that the theory is not quite right and has to be worked over again, very much as any other work of art—a painting, a sculpture has to be worked over in the interests of aesthetic perfection. So there is no scientist who is not to some extent worthy of being described as artist or poet.

There is a theory that creativity arises when individuals are out of sync with their environment. To put it simply, people who fit in with their communities have insufficient motivation to risk their psyches in creating something truly new, while those who are out of sync are driven by the constant need to prove their worth.

In 'Beyond the Soapsuds Universe', Discover Magazine (1997). The author explains (in a blog found online) that this “idea comes from a theory by Mihaly Csikszentmihalyi, who wrote a book called Flow: the Psychology of Optimal Experience. You do need someone to come in from outside. One of the theories about why mathematicians do their best work when they’re young is because they’re not yet educated enough to know what seems obviously wrong. So they try new things.”

There is an attraction and a charm inherent in the colossal that is not subject to ordinary theories of art ... The tower will be the tallest edifice ever raised by man. Will it therefore be imposing in its own way?

Quoted in J. Harriss, The Tallest Tower: Eiffel and the Belle Epoque (1975), 25. Cited by David P. Billington, 'Bridges and the New Art of Structural Engineering,' in National Research Council (U.S.). Transportation Research Board Subcommittee on Bridge Aesthetics, Bridge Aesthetics Around the World (1991), 67.

There is no great harm in the theorist who makes up a new theory to fit a new event. But the theorist who starts with a false theory and then sees everything as making it come true is the most dangerous enemy of human reason.

There is no more convincing proof of the truth of a comprehensive theory than its power of absorbing and finding a place for new facts, and its capability of interpreting phenomena which had been previously looked upon as unaccountable anomalies. It is thus that the law of universal gravitation and the undulatory theory of light have become established and universally accepted by men of science. Fact after fact has been brought forward as being apparently inconsistent with them, and one alter another these very facts have been shown to be the consequences of the laws they were at first supposed to disprove. A false theory will never stand this test. Advancing knowledge brings to light whole groups of facts which it cannot deal with, and its advocates steadily decrease in numbers, notwithstanding the ability and scientific skill with which it may have been supported.

From a review of four books on the subject 'Mimicry, and Other Protective Resemblances Among Animals', in The Westminster Review (Jul 1867), 88, 1. Wallace is identified as the author in the article as reprinted in William Beebe, The Book of Naturalists: An Anthology of the Best Natural History (1988), 108.

There is no such thing as absolute truth and absolute falsehood. The scientific mind should never recognise the perfect truth or the perfect falsehood of any supposed theory or observation. It should carefully weigh the chances of truth and error and grade each in its proper position along the line joining absolute truth and absolute error.

There is now a feeling that the pieces of physics are falling into place, not because of any single revolutionary idea or because of the efforts of any one physicist, but because of a flowering of many seeds of theory, most of them planted long ago.

Therefore on long pondering this uncertainty of mathematical traditions on the deduction of the motions of the system of the spheres, I began to feel disgusted that no more certain theory of the motions of the mechanisms of the universe, which has been established for us by the best and most systematic craftsman of all, was agreed by the philosophers, who otherwise theorised so minutely with most careful attention to the details of this system. I therefore set myself the task of reading again the books of all philosophers which were available to me, to search out whether anyone had ever believed that the motions of the spheres of the, universe were other than was supposed by those who professed mathematics in the schools.

These results demonstrate that there is a new polymerase inside the virions of RNA tumour viruses. It is not present in supernatents of normal cells but is present in virions of avian sarcoma and leukemia RNA tumour viruses. The polymerase seems to catalyse the incorporation of deoxyrinonucleotide triphosphates into DNA from an RNA template. Work is being performed to characterize further the reaction and the product. If the present results and Baltimore's results with Rauscher leukemia virus are upheld, they will constitute strong evidence that the DNA proviruses have a DNA genome when they are in virions. This result would have strong implications for theories of viral carcinogenesis and, possibly, for theories of information transfer in other biological systems. [Co-author with American virologist Satoshi Mizutani]

This incomparable Author having at length been prevailed upon to appear in public, has in this Treatise given a most notable instance of the extent of the powers of the Mind; and has at once shown what are the Principles of Natural Philosophy, and so far derived from them their consequences, that he seems to have exhausted his Argument, and left little to be done by those that shall succeed him.a

This theory [the oxygen theory] is not as I have heard it described, that of the French chemists, it is mine (elle est la mienne); it is a property which I claim from my contemporaries and from posterity.

This very important property of rods, and indeed also of each kind of cone, this limitation of output to a single dimension of change, may be called the Principle of Univariance and stated thus: “The output of a receptor depends upon its quantum catch, but not upon what quanta are caught.” … Young's theory of colour vision may now be stated in terms of cone pigments. “There are three classes of cone each containing a different visual pigment. The output of each cone is univariant, depending simply upon the quantum catch of its pigment. Our sensation of colour depends upon the ratios of these three cone outputs.”

Principle of Univariance, concerning color vision, as stated in Lecture to a meeting of the Physiological Society at Chelsea College, London (17 Apr 1970), and reported in 'Pigments and Signals in Colour Vision', The Journal of Physiology (1972), 220 No. 3, 4P.

Those who knew that the judgements of many centuries had reinforced the opinion that the Earth is placed motionless in the middle of heaven, as though at its centre, if I on the contrary asserted that the Earth moves, I hesitated for a long time whether to bring my treatise, written to demonstrate its motion, into the light of day, or whether it would not be better to follow the example of the Pythagoreans and certain others, who used to pass on the mysteries of their philosophy merely to their relatives and friends, not in writing but by personal contact, as the letter of Lysis to Hipparchus bears witness. And indeed they seem to me to have done so, not as some think from a certain jealousy of communicating their doctrines, but so that their greatest splendours, discovered by the devoted research of great men, should not be exposed to the contempt of those who either find it irksome to waste effort on anything learned, unless it is profitable, or if they are stirred by the exhortations and examples of others to a high-minded enthusiasm for philosophy, are nevertheless so dull-witted that among philosophers they are like drones among bees.

Though the theories of plate tectonics now provide us with a modus operandi, they still seem to me to be a periodic phenomenon. Nothing is world-wide, but everything is episodic. In other words, the history of any one part of the earth, like the life of a soldier, consists of long periods of boredom and short periods of terror.

Throughout the last four hundred years, during which the growth of science had gradually shown men how to acquire knowledge of the ways of nature and mastery over natural forces, the clergy have fought a losing battle against science, in astronomy and geology, in anatomy and physiology, in biology and psychology and sociology. Ousted from one position, they have taken up another. After being worsted in astronomy, they did their best to prevent the rise of geology; they fought against Darwin in biology, and at the present time they fight against scientific theories of psychology and education. At each stage, they try to make the public forget their earlier obscurantism, in order that their present obscurantism may not be recognized for what it is.

Thus with every advance in our scientific knowledge new elements come up, often forcing us to recast our entire picture of physical reality. No doubt, theorists would much prefer to perfect and amend their theories rather than be obliged to scrap them continually. But this obligation is the condition and price of all scientific progress.

To come very near to a true theory, and to grasp its precise application, are two different things, as the history of science teaches us. Everything of importance has been said before by someone who did not discover it.

To connect the dinosaurs, creatures of interest to everyone but the veriest dullard, with a spectacular extra­terrestrial event like the deluge of meteors … seems a little like one of those plots that a clever publisher might concoct to guarantee enormous sales. All the Alvarez-Raup theories lack is some sex and the involvement of the Royal family and the whole world would be paying attention to them.

To produce a really good biological theory one must try to see through the clutter produced by evolution to the basic mechanisms lying beneath them, realizing that they are likely to be overlaid by other, secondary mechanisms. What seems to physicists to be a hopelessly complicated process may have been what nature found simplest, because nature could only build on what was already there.

To say that, a scientific man puts forth a theory and, supports it and adheres to it, not because he thinks it true, but because he wishes it to be true, is the same thing as saying that he is not a seeker after truth at all, and is therefore a traitor to his profession.

To trace the series of these revolutions, to explain their causes, and thus to connect together all the indications of change that are found in the mineral kingdom, is the proper object of a THEORY OF THE EARTH.

To turn Karl [Popper]'s view on its head, it is precisely the abandonment of critical discourse that marks the transition of science. Once a field has made the transition, critical discourse recurs only at moments of crisis when the bases of the field are again in jeopardy. Only when they must choose between competing theories do scientists behave like philosophers.

Today scientists describe the universe in terms of two basic partial theories—the general theory of relativity and quantum mechanics. They are the great intellectual achievements of the first half of this century. The general theory of relativity describes the force of gravity and the large-scale structure of the universe, that is, the structure on scales from only a few miles to as large as a million million million million (1 with twenty-four zeros after it) miles, the size of the observable universe. Quantum mechanics, on the other hand, deals with phenomena on extremely small scales, such as a millionth of a millionth of an inch. Unfortunately, however, these two theories are known to be inconsistent with each other—they cannot both be correct.

Understanding a theory has, indeed, much in common with understanding a human personality. We may know or understand a man's system of dispositions pretty well; that is to say, we may be able to predict how he would act in a number of different situations. But since there are infinitely many possible situations, of infinite variety, a full understanding of a man's dispositions does not seem to be possible.

Until now, physical theories have been regarded as merely models with approximately describe the reality of nature. As the models improve, so the fit between theory and reality gets closer. Some physicists are now claiming that supergravity is the reality, that the model and the real world are in mathematically perfect accord.

We called the new [fourth] quark the “charmed quark” because we were pleased, and fascinated by the symmetry it brought to the subnuclear world. “Charm” also means a “a magical device to avert evil,” and in 1970 it was realized that the old three quark theory ran into very serious problems. ... As if by magic the existence of the charmed quark would [solve those problems].

From asppearance in the BBC-TV program written by Nigel Calder, 'The Key to the Universe,' (27 Jan 1977). As cited in Arthur Lewis Caso, 'The Production of New Scientific Terms', American Speech (Summer 1980), 55, No. 2, 102.

We cannot see how the evidence afforded by the unquestioned progressive development of organised existence—crowned as it has been by the recent creation of the earth's greatest wonder, MAN, can be set aside, or its seemingly necessary result withheld for a moment. When Mr. Lyell finds, as a witty friend lately reported that there had been found, a silver-spoon in grauwacke, or a locomotive engine in mica-schist, then, but not sooner, shall we enrol ourselves disciples of the Cyclical Theory of Geological formations.

We have decided to call the entire field of control and communication theory, whether in the machine or in the animal, by the name Cybernetics, which we form from the Greek … for steersman. In choosing this term, we wish to recognize that the first significant paper on feedback mechanisms is an article on governors, which was published by Clerk Maxwell in 1868, and that governor is derived from a Latin corruption … We also wish to refer to the fact that the steering engines of a ship are indeed one of the earliest and best-developed forms of feedback mechanisms.

We have found that where science has progressed the farthest, the mind has but regained from nature that which the mind has put into nature.We have found a strange foot-print on the shores of the unknown. We have devised profound theories, one after another, to account for its origin. At last, we have succeeded in reconstructing the creature that made the foot-print. And Lo! it is our own.

We have the satisfaction to find, that in nature there is wisdom, system and consistency. For having, in the natural history of this earth, seen a succession of worlds, we may from this conclude that, there is a system in nature; in like manner as, from seeing revolutions of the planets, it is concluded, that there is a system by which they are intended to continue those revolutions. But if the succession of worlds is established in the system of nature, it is vain to look for anything higher in the origin of the earth. The result, therefore, of our present enquiry is, that we find no vestige of a beginning,-no prospect of an end.

We lay down a fundamental principle of generalization by abstraction: The existence of analogies between central features of various theories implies the existence of a general theory which underlies the particular theories and unifies them with respect to those central features.

We may affirm of Mr. Buffon, that which has been said of the chemists of old; though he may have failed in attaining his principal aim, of establishing a theory, yet he has brought together such a multitude of facts relative to the history of the earth, and the nature of its fossil productions, that curiosity finds ample compensation, even while it feels the want of conviction.

We regard as 'scientific' a method based on deep analysis of facts, theories, and views, presupposing unprejudiced, unfearing open discussion and conclusions. The complexity and diversity of all the phenomena of modern life, the great possibilities and dangers linked with the scientific-technical revolution and with a number of social tendencies demand precisely such an approach, as has been acknowledged in a number of official statements.

We see, then, that the elements of the scientific method are interrelated. Facts are necessary materials; but their working up by experimental reasoning, i.e., by theory, is what establishes and really builds up science. Ideas, given form by facts, embody science. A scientific hypothesis is merely a scientific idea, preconceived or previsioned. A theory is merely a scientific idea controlled by experiment. Reasoning merely gives a form to our ideas, so that everything, first and last, leads back to an idea. The idea is what establishes, as we shall see, the starting point or the primum movens of all scientific reasoning, and it is also the goal in the mind's aspiration toward the unknown.

Well-established theories collapse under the weight of new facts and observations which cannot be explained, and then accumulate to the point where the once useful theory is clearly obsolete.[Using Thomas S. Kuhn's theories to frame his argument about the relationship beween science and technology: as new facts continue to accumulate, a new, more accurate paradigm must replace the old one.]

Were I disposed to consider the comparative merit of each of them [facts or theories in medical practice], I should derive most of the evils of medicine from supposed facts, and ascribe all the remedies which have been uniformly and extensively useful, to such theories as are true. Facts are combined and rendered useful only by means of theories, and the more disposed men are to reason, the more minute and extensive they become in their observations

What I remember most clearly was that when I put down a suggestion that seemed to me cogent and reasonable, Einstein did not in the least contest this, but he only said, 'Oh, how ugly.' As soon as an equation seemed to him to be ugly, he really rather lost interest in it and could not understand why somebody else was willing to spend much time on it. He was quite convinced that beauty was a guiding principle in the search for important results in theoretical physics.

What is important is the gradual development of a theory, based on a careful analysis of the ... facts. ... Its first applications are necessarily to elementary problems where the result has never been in doubt and no theory is actually required. At this early stage the application serves to corroborate the theory. The next stage develops when the theory is applied to somewhat more complicated situations in which it may already lead to a certain extent beyond the obvious and familiar. Here theory and application corroborate each other mutually. Beyond lies the field of real success: genuine prediction by theory. It is well known that all mathematized sciences have gone through these successive stages of evolution.

What the founders of modern science, among them Galileo, had to do, was not to criticize and to combat certain faulty theories, and to correct or to replace them by better ones. They had to do something quite different. They had to destroy one world and to replace it by another. They had to reshape the framework of our intellect itself, to restate and to reform its concepts, to evolve a new approach to Being, a new concept of knowledge, a new concept of science—and even to replace a pretty natural approach, that of common sense, by another which is not natural at all.

Wheeler hopes that we can discover, within the context of physics, a principle that will enable the universe to come into existence “of its own accord.” In his search for such a theory, he remarks: “No guiding principle would seem more powerful than the requirement that it should provide the universe with a way to come into being.” Wheeler likened this 'self-causing' universe to a self-excited circuit in electronics.

When an investigator has developed a formula which gives a complete representation of the phenomena within a certain range, he may be prone to satisfaction. Would it not be wiser if he should say “Foiled again! I can find out no more about Nature along this line.”

When I read some forty years ago that shells from Syria were found in the Alpes, I said, I admit, in a rather joking way, that these shells had apparently been carried by pilgrims on their return from Jerusalem. Mr. Buffon reprimanded me rather sharply in his Theory of the Earth, p. 28 I. I did not want to lose his friendship for peanuts; however, I am still of the same opinion because the impossibility of the formation of mountains by the sea is demonstrated to me.

Wherever possible, scientists experiment. Which experiments suggest themselves often depends on which theories currently prevail. Scientists are intent of testing those theories to the breaking point. They do not trust what is intuitively obvious. That the Earth is flat was once obvious. That heavy bodies fall faster than light ones was once obvious. That bloodsucking leeches cure most diseases was once obvious. That some people are naturally and by divine decree slaves was once obvious. That there is such a place as the center of the Universe, and that the Earth sits in that exalted spot was once obvious. That there is an absolute standard of rest was once obvious. The truth may be puzzling or counterintuitive. It may contradict deeply held beliefs. Experiment is how we get a handle on it.

Whether statistics be an art or a science... or a scientific art, we concern ourselves little. It is the basis of social and political dynamics, and affords the only secure ground on which the truth or falsehood of the theories and hypotheses of that complicated science can be brought to the test.

Who ... is not familiar with Maxwell's memoirs on his dynamical theory of gases? ... from one side enter the equations of state; from the other side, the equations of motion in a central field. Ever higher soars the chaos of formulae. Suddenly we hear, as from kettle drums, the four beats 'put n=5.' The evil spirit v vanishes; and ... that which had seemed insuperable has been overcome as if by a stroke of magic ... One result after another follows in quick succession till at last ... we arrive at the conditions for thermal equilibrium together with expressions for the transport coefficients.

Why has not anyone seen that fossils alone gave birth to a theory about the formation of the earth, that without them, no one would have ever dreamed that there were successive epochs in the formation of the globe.

Discours sur les révolutions du globe, (Discourse on the Revolutions of the Surface of the Globe), originally the introduction to Recherches sur les ossemens fossiles des quadrupèdes (1812). Translated by Ian Johnston from the 1825 edition. Online at Vancouver island University website.

In discourse delivered before the British Association at Liverpool (16 Sep 1870), 'Scientific Use of the Imagination', collected in Fragments of Science: a Series of Detached Essays, Addresses and Reviews (1892), Vol. 2, 104.

With all reserve we advance the view that a supernova represents the transition of an ordinary star into a neutron star consisting mainly of neutrons. Such a star may possess a very small radius and an extremely high density. As neutrons can be packed much more closely than ordinary nuclei and electrons, the gravitational packing energy in a cold neutron star may become very large, and under certain conditions may far exceed the ordinary nuclear packing fractions...[Co-author with Walter Baade]

Paper presented to American Physical Society meeting at Stanford (15-16 Dec 1933). Published in Physical Review (15 Jan 1934). Cited in P. Haensel, Paweł Haensel and A. Y. Potekhin, D. G. Yakovlev, Neutron Stars: Equation of State and Structure (2007), 2-3. Longer version of quote from Freeman Dyson, From Eros to Gaia (1992), 34. The theoretical prediction of neutron stars was made after analyzing observations of supernovae and proposed as an explanation of the enormous energy released in such explosions. It was written just two years after Chadwick discovered the neutron.

With whom [do] the adherents of historicism actually empathize[?] The answer is inevitable: with the victor. And all rulers are the heirs of those who conquered before them. Hence, empathy with the victor invariably benefits the rulers. Historical materialists know what that means. Whoever has emerged victorious participates to this day in the triumphal procession in which the present rulers step over those who are lying prostrate. According to traditional practice, the spoils are carried along in the procession. They are called cultural treasures, and a historical materialist views them with cautious detachment. For without exception the cultural treasures he surveys have an origin which he cannot contemplate without horror. They owe their existence not only to the efforts of the great minds and talents who have created them, but also to the anonymous toil of their contemporaries. There is no document of civilization which is not at the same time a document of barbarism.

Without preparing fluorine, without being able to separate it from the substances with which it is united, chemistry has been able to study and to analyze a great number of its compounds. The body was not isolated, and yet its place was marked in our classifications. This well demonstrates the usefulness of a scientific theory, a theory which is regarded as true during a certain time, which correlates facts and leads the mind to new hypotheses, the first causes of experimentation; which, little by little, destroy the theory itself, in order to replace it by another more in harmony with the progress of science.[Describing the known history of fluorine compounds before his isolation of the element.]

'Fluorine', lecture at the Royal Institution (28 May 1897), translated from the French, in Proceedings of the Royal Institution (1897). In Annual Report of the Board of Regents of the Smithsonian Institution to July 1897 (1898), 262.

Without theory, practice is but routine born of habit. Theory alone can bring forth and develop the spirit of invention. ... [Do not] share the opinion of those narrow minds who disdain everything in science which has not an immediate application. ... A theoretical discovery has but the merit of its existence: it awakens hope, and that is all. But let it be cultivated, let it grow, and you will see what it will become.

Inaugural Address as newly appointed Professor and Dean (Sep 1854) at the opening of the new Faculté des Sciences at Lille (7 Dec 1854). In René Vallery-Radot, The Life of Pasteur, translated by Mrs. R. L. Devonshire (1919), 76.

Yet the widespread [planetary theories], advanced by Ptolemy and most other [astronomers], although consistent with the numerical [data], seemed likewise to present no small difficulty. For these theories were not adequate unless they also conceived certain equalizing circles, which made the planet appear to move at all times with uniform velocity neither on its deferent sphere nor about its own [epicycle's] center … Therefore, having become aware of these [defects], I often considered whether there could perhaps be found a more reasonable arrangement of circles, from which every apparent irregularity would be derived while everything in itself would move uniformly, as is required by the rule of perfect motion.

You make experiments and I make theories. Do you know the difference? A theory is something nobody believes, except the person who made it. An experiment is something everybody believes, except the person who made it.Remark to Hermann F. Mark.

Your remarks upon chemical notation with the variety of systems which have arisen, &c., &c., had almost stirred me up to regret publicly that such hindrances to the progress of science should exist. I cannot help thinking it a most unfortunate thing that men who as experimentalists & philosophers are the most fitted to advance the general cause of science & knowledge should by promulgation of their own theoretical views under the form of nomenclature, notation, or scale, actually retard its progress.

Letter to William Whewell (21 Feb 1831). In Isaac Todhunter, William Whewell, An Account of his Writings (1876), Vol. 1., 307. Faraday may have been referring to a paper by Whewell published in the Journal of the Royal Institution of England (1831), 437-453.

Your theories are those which you and many other people find easiest and pleasantest to believe, but, so far as I can see, they have no foundation other than they lead to a pleasant view of life … I agree that faith is essential to success in life … but I do not accept your definition of faith, i.e. belief in life after death. In my view, all that is necessary for faith is the belief that by doing our best we shall come nearer to success and that success in our aims (the improvement of the lot of mankind, present and future) is worth attaining … I maintain that faith in this world is perfectly possible without faith in another world.

[Alfred Russell] Wallace's sales agent, back in London, heard mutterings from some naturalists that young Mr. Wallace ought to quit theorizing and stick to gathering facts. Besides expressing their condescension toward him in particular, that criticism also reflected a common attitude that fact-gathering, not theory, was the proper business of all naturalists.

From movie The 30-foot Bride of Candy Rock (1959). Writers, Rowland Barber and Arthur A. Ross. In Larry Langman and Paul Gold, Comedy Quotes from the Movies (2001), 289. This movie, (with its rare appearance of Costello without Bud Abott, his usual comedy partner), was released later in the year of Costello's death.

[Kepler] had to realize clearly that logical-mathematical theoretizing, no matter how lucid, could not guarantee truth by itself; that the most beautiful logical theory means nothing in natural science without comparison with the exactest experience. Without this philosophic attitude, his work would not have been possible.

[Modern science] passed through a long period of uncertainty and inconclusive experiment, but as the instrumental aids to research improved, and the results of observation accumulated, phantoms of the imagination were exorcised, idols of the cave were shattered, trustworthy materials were obtained for logical treatment, and hypotheses by long and careful trial were converted into theories.

[The infinitely small] neither have nor can have theory; it is a dangerous instrument in the hands of beginners [ ... ] anticipating, for my part, the judgement of posterity, I would dare predict that this method will be accused one day, and rightly, of having retarded the progress of the mathematical sciences.